MODEL   DRHiflZING 


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taiTTjed  below. 


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LOS  AiN'GELES 
UBRARY 


MODEL    DRAWING 

PKEPARED  FOR  THE  USE  OF  THE  STUDENTS 


OF    THE 


Massachusetts  normal  Art  School, 


BOSTOK,  MASS. 


By  ANSON  K.  CROSS. 


BOSTOiT: 

1890. 


J  J      J  ,  ,^  -"  o 


'^'(^S^ 


COPTEIonTKD   BT 

ANSON   K.  CROSS. 
1830, 


i  > 


6,    \  5 

INTRODUCTIOK 


The  value  of  a  course  in  dra'wing  when,  the  subject  is 
properly  presented  to  the  student  can  scarcely  be  over- 
estimated, but  it  must  be  confessed  that  much  of  the 
instruction  given  is  such  that  its  benefit  is  a  matter  of 
doubt.  At  the  beginning  of  his  art  education  the  student 
should  be  taught  to  see  correctly.  When  this  has  been 
accomplished,  and  he  is  able  to  represent  truly  what  is 
before  him  as  it  appears,  and  not  as  he  thinks  he  sees  it, 
then  he  is  in  a  position  to  advance,  and  his  imagination 
may  be  cultivated.  But  as  the  first  point  to  be  gained  is 
ability  to  see  truly,,  it  follows  that  we  should  from  the 
very  start  demand  truth ;  first  truth  of  outline,  next,  truth 
of  light  and  shade,  and  then  truth  of  color.  We  wish  to 
consider  here  simply  truth  of  outline,  but  the  student  will 
find  that  the  study  of  appearances,  and  their  representation 
as  fully  as  possible,  even  in  so  simple  a  medium  as  outline, 
will  have  in  great  measure  prepared  the  way  for  the  more 
difficult  work  in  light  and  shade  and  color.  The  whole 
question  is  simply  one  of  seeing,  and  the  student  should 
not  trouble  himself  over  technique,  as  he  has  enough  to  do 
to  represent  nature  truly. 

It  is  often  said  that  in  nature  there  are  no  outlines.  In  a 
way  this  is  true,  but  it  cannot  be  understood  to  mean  that 

(3) 


4  INTRODUCTION. 

form  is  unnecessary  or  that  it  may  be  slighted.  The  stu- 
dent cannot  learn  to  paint  or  to  make  pictures  in  any  me- 
dium without  drawing  the  forms  of  the  objects.  The 
defining  of  the  lights  and  shades  and  the  various  bits  of 
color  which  go  to  make  the  effect,  is  necessary  to  give 
solidity  and  character  to  a  picture,  and  it  is  useless  to  think 
that  anything  can  be  accomplished  with  color  or  light  and 
shade  until  exact  representations  of  form  can  be  made. 

Every  object  has  definite  form  and  size,  and  though  it 
may  not  be  outlined  it  has  boundaries.  Although  the  rep- 
resentation of  objects  in  outline  only  is  at  best  a  conven- 
tional and  imperfect  means  of  expression,  so  far  often  as 
even  form  is  concerned,  the  student  can  be  taught  to  ob- 
serve effects  and  may  succeed  in  conveying  a  fair  impres- 
sion of  the  character  of  the  object  and  of  varieties  of 
surface  and  texture. 

The  student  must  work  long  and  earnestly  before 
he  can  separate  facts  from  appearances,  as  the  knowledge 
of  the  actual  form  prevents  the  mind  from  accepting 
its  appearance.  The  impression  conveyed  to  the  mind 
of  one  not  trained  to  accept  the  vision  of  the  eye,  is 
the  result  of  a  combination  of  what  the  eye  sees  with  what 
is  by  far  the  greatest  factor,  what  the  mind  knows  con- 
cerning the  actual  condition  of  the  object.  The  student 
must  struggle  continually  not  only  against  this  influence 
of  his  mind,  but  also  against  the  effect  which  one  line 
exerts  to  change  the  apparent  direction  of  others.  This 
effect  is  sometimes  so  strong  that  even  the  practised  eye  of 
the  artist  is  deceived,  and  we  may  safely  say  that  the  most 


INTRODUCTION.  O 

perfect  eye,  with  the  longest  training  (of  sketching  simply) 
is  not  surety  against  mistakes.  A  knowledge  of  the  per- 
spective principles  governing  the  appearance  of  form  is 
thus  absolutely  necessary  to  the  draughtsman  who  would 
be  exact,  and  there  is  no  reason  why  there  should  not  be 
exactness  and  artistic  rendering  at  the  same  time. 


MODEL    DRAWING. 


FREEHAND  DRAWING. 

The  most  important  points  in  freehand  drawing  are  free- 
dom, directness  and  accuracy.  It  is  difficult  to  give  direc- 
tions which  shall  produce  these  results,  as  individuality- 
will  prevent  all  from  working  in  a  uniform  way,  and  hand- 
ling and  technique  are  of  little  importance.  Since  the  pro- 
duction of  correct  drawings  is  the  end  desired,  it  is  of  no 
consequence  that  such  drawings  are  produced  by  different 
persons  in  different  ways,  but  it  may  be  well  to  give  a  few 
general  directions,  the  most  important  being  that  the  pencil 
should  be  held  lightly,  and  the  first  lines  of  the  drawing 
sketched  in  freely  and  very  quickly.  The  paper  should  be 
not  less  than  eleven  by  fifteen  inches,  and  the  drawings 
should  be  large.  In  beginning,  it  will  be  best  to  draw  the 
full  size  of  the  objects,  as  small  drawings  will  produce  a 
cramped  way  of  working.  A  long  pencil  will  assist 
the  student  to  freedom  of  movement.  It  may  be  held 
as  a  stick  of  charcoal  between  the  thumb  and  first 
two  fingers,  and  as  far  from  the  point  as  possible.  The 
paper  should  be  fastened  to  the  board,  witli  its  edges  paral- 
lel to  those  of  the  board.  If  the  edge  of  the  paper  is  not 
quite  straight,  a  horizontal  line  should  be  ruled  near  the 
lower  edge,  so  that  directions  may  be  referred  to  this  line. 

(6) 


SIXGLE    OBJECTS.  7 

Before  attempting  to  represent  any  object,  the  student 
should  acquire  the  freedom  of  motion  which  is  necessary 
to  good  work,  by  drawing  lines  in  all  directions.  Curved 
lines  will  be  produced  by  swinging  the  pencil  from  the 
wrist,  elbow  or  shoulder,  and  straight  lines  by  a  motion  of 
the  entire  arm.  This  movement  should  be  practised  until 
lines  can  be  drawn  instantly  across  the  paper  in  any  direc- 
tion. This  free  motion  is  most  important  for  all  sketching, 
but  in  finishing  or  lining  in  a  drawing  whose  proportions 
have  been  thus  sketched,  more  pressure  will  be  required, 
and  the  pencil  may  be  held  more  firmly  and  nearer  the 
point. 

The  first  subjects  should  be  the  geometric  solids,  with 
the  vase  forms  (such  as  are  found  in  the  models  to  be  ob- 
tained at  Art  Supply  Stores),  but  common  objects,  as  boxes, 
etc.,  are  equally  good.  We  will  explain  the  way  in  which 
these  should  be  studied,  by  making  a  sketch  from  a  box 
with  its  cover  partly  open  (Fig.  1).  First,  nearly  close  the 
eyes,  and  try  to  see  the  box  not  as  a  solid,  but  as  a  sil- 
houette, the  outline  of  the  mass  of  the  box,  as  seen  against 
the  background,  being  what  should  first  be  carefully  studied. 
A  little  practise  with  the  eyes  nearly  closed  will  enable  one 
to  see  the  mass  in  this  way.  In  order  to  see  the  direction 
which  the  edges  appear  to  have,  lines  may  be  drawn  in  the 
air  by  moving  the  pencil  point  so  that  it  passes  in  front  of 
the  edges.  Care  should  be  taken  not  to  move  the  pencil 
away  from  the  eye  when  this  is  done,  that  is  in  the  actual 
direction  of  the  edges,  but  to  keep  the  pencil  point  where 
it  would  be  if  it  were  held  upon  a  pane  of  glass  placed 


8  SINGLE    OBJECTS. 

directly  in  front  of  the  student.  This  test  is  the  most 
valuable  of  all,  because  it  is  the  easiest  and  simplest  to 
apply.  It  is  really  the  same  as  the  one  of  the  thread 
explained  on  page  59,  and  nearly  all  other  means  of  testing 
will  at  last  be  discarded  in  favor  of  this  first  and  simplest. 
After  careful  study  of  the  mass,  its  outline  may  be  lightly 
sketched,  no  measurements  of  any  kind  having  been  made. 
The  aim  is  to  train  the  eye  to  exact  seeing,  and  in  order  to 
do  this  the  student  must  learn  to  depend  on  his  eye,  and 
put  down  its  impression  rather  than  the  results  of  mechani- 
cal tests  of  proportion.  We  must  draw  first,  and  afterwards 
test  hy  measuring.  When  the  outline  of  the  mass  has  been 
sketched  then  the  inner  lines  may  be  drawn,  and  the  result 
carefully  studied  to  see  that  it  agrees  with  the  appearance. 
When  it  is  as  near  as  can  be  seen,  it  may  be  tested  by 
measuring  the  proportions,  as  explained  on  page  53.  If  the 
sketch  does  not  agree  with  these  tests  it  must  be  changed. 
All  changes  are  to  be  made  not  by  erasing,  but  by  drawing 
new  lines,  and  the  drawing  must  be  carried  on  in  this  way 
until  the  correct  lines  are  determined.  The  first  lines 
must  be  very  light,  and  as  changes  are  made  the  strength 
must  be  increased  to  distinguish  them,  until  the  correct  line 
is  secured.  The  drawing  now  having  been  changed  to  agree 
with  the  measurement  of  the  whole  height  and  width,  and 
tested  by  moving  the  pencil  point  to  cover  the  edges,  it  will 
be  well  to  test  it  by  means  of  vertical  and  horizontal  lines 
passing  through  all  the  angles  of  the  box.  Thus  drop  the 
pencil  point  vertically  from  point  1,  and  see  where  it  cuts 
the  lower  edge,  and  carry  the  point  horizontally  from  2, 


SINGLE    OBJECTS.  9 

and  note  its  intersection  with  the  front  edge.  When  these 
tests  have  been  made,  the  pencil  point  may  be  moved  to 
cover,  and  made  to  continue  the  edges  A,  B,  C,  etc.,  until 
the  points  where  they  cut  the  opposite  outline  are  noted. 
These  tests  may  also  be  applied  by  the  pencil  held  hori- 
zontal and  vertical,  and  used  as  a  straight  edge  to  continue 
lines.  Such  tests,  if  carefully  made,  should  give  a  drawing 
practically  correct,  and  should  be  depended  upon  with  the  first 
measurement  of  the  whole  height  and  width,  which  should 
be  very  carefully  taken.  Any  distances  which  are  nearly 
equal,  as  E,  F,  and  F,  G,  may  also  be  compared,  but  as  a 
rule  very  few  measurements  of  proportion  should  be  made, 
as  short  measurements,  or  a  short  with -a  long,  cannot  be 
made  with  sufficient  accuracy  to  be  of  any  value.  The 
thread  may  be  used  instead  of  the  pencil  in  making  these 
tests,  as  explained  on  page  59.  The  thread  gives  a  fine 
line,  and  its  intersections  with  the  various  edges  can  be 
seen  exactly,  so  that  until  the  eye  can  be  very  closely  de- 
pended upon  the  thread  is  preferable  to  the  pencil.  In  all 
of  this  work  the  changes  must  be  made  hy  drawing  new 
lines  and  not  hy  erasing.  This  is  most  important,  for  the 
erasing  of  lines  and  thus  the  keeping  of  but  one  line 
throughout  the  various  stages  is  most  certain  to  produce  a 
hard  and  inaccurate  drawing,  and  even  although  it  may 
finally  be  made  to  agree  with  all  tests,  it  will  still  be  lack- 
ing in  spirit. 

It  is  very  difficult  for  most  students  to  draw  lightly 
enough  to  secure  the  correct  result  except  in  very  black 
lines,  but  it  is  better  rather  than  to  erase  to  throw  the 


10  SIXGLE    OBJECTS. 

drawing  away  and  start  anew,  until  the  correct  lines  can 
be  secured  without  too  great  heaviness.  The  reason  for 
this  way  of  Avorking  is,  that  we  wish  the  student  to  depend 
as  much  as  possible  on  his  eyes,  and  if  he  erases,  and  has 
one  line  from  the  beginning,  unnecessary  time  is  given  to 
its  drawing,  and  he  will  hesitate  before  erasing  it.  If  light 
lines  are  drawn  and  not  erased,  but  others  drawn  as  soon  as 
there  is  doubt  about  the  first  being  rightly  placed,  the  stu- 
dent is  much  more  free  to  change  as  each  suggestion  occurs, 
and  toward  the  last  he  has  his  choice  (as  the  tests  indicate 
corrections)  of  the  various  lines  already  drawn.  This  is  by 
far  the  quickest  and  most  accurate  way,  and  besides  it 
prepares  for  quick  and  accurate  sketching ;  indeed  the 
student  will  not  have  to  draw  very  long  from  the  geometric 
solids  before  he  will  be  able  to  produce  correct  sketches 
without  drawing  many  unnecessary  lines. 

There  is  not  much  choice  of  pencils  for  this  part  of  the 
work,  but  it  is  well  to  use  always  as  soft  a  one  as  the 
nature  of  the  work  will  permit.  As  no  pressure  should 
be  used,  the  lead  barely  making  a  mark  on  the  surface  of 
the  paper,  and  as  all  the  lines  except  the  correct  ones  must 
be  erased,  there  is  no  reason  why  the  student  who  has  diifi- 
culty  with  the  soft  pencil  should  not  use  a  hard  one  until 
the  drawing  is  ready  to  line  in. 

When  the  correct  outline  has  been  found,  it  is  necessary 
to  finish  the  drawing.  The  paper  must  first  be  cleaned,  all 
the  lines  except  the  correct  ones  being  erased.  The  easiest 
way  to  reserve  these  lines  will  be  to  make  them  enough 
stronger  than  the  others,  so  that  they  will  show  faintly 


SINGLE    OBJECTS.  11 

when  the  latter  have  been  removed.  The  drawing  may 
now  be  lined  in  with  a  soft  pencil  (and  here  the>  pencil 
must  be  held  more  firmly  and  nearer  the  point),  the  attempt 
being  not  to  produce  a  fine,  even  line,  in  imitation  of  a  ruled 
one,  but  rather  a  line  of  medium  strength,  which  may  be 
easily  drawn,  and  shall  convey  the  idea  of  straight,  un- 
broken edges.  For  the  present  it  is  better  for  the  lines  to 
be  made  of  one  strength,  with  no  attempt  at  gradation,  or 
the  frequent  conventional  lining  in  of  the  nearer  edges  in 
heavier  lines.  This  point  will  be  considered  later,  but  we 
wish  now  to  advise  the  student,  if  he  is  already  familiar 
with  it,  to  forget  it  as  quickly  as  possible,  and  to  finish  in 
uniform  lines  or  in  the  way  explained  on  page  17. 

The  method  of  work  presented  in  these  notes  is  that 
which  should  always  be  employed,  and  the  student  should 
draw  from  various  objects,  in  different  positions,  until  he  is 
able  to  see  them  very  nearly  correct  at  first.  The  time 
required  for  this  will  depend  wholly  upon  the  pupil,  and 
the  care  with  which  directions  are  followed. 


GROUPS. 

After  the  practise  from  single  objects,  prisms,  pyramids, 
etc.,  two  or  three  should  be  placed  together,  and  here  the 
method  is  the  same  as  for  a  single  object.  The  usual  way, 
or  that  which  the  student  would  probably  adopt,  would  be 
to  draw,  first  the  prism  A,  fig.  4 ;  next  the  vase  B ;  then 
the  cylinder  C  ;  and  last  the  frame  D.  The  trouble  with  this 
way  of  proceeding  is  that  the  objects  are  drawn  one  at  a 
time,  and  one  added  to  the  others,  so  that  until  the  last  is 
drawn  the  proportion  of  the  whole  group,  that  is,  the 
greatest  width  in  comparison  with  the  greatest  height,  can- 
not be  seen.  Indeed,  this  is  often  not  even  considered,  the 
student  taking  it  for  granted  that  since  he  has  measured  and 
tested  each  object  as  he  drew  it,  the  single  objects  are  cor- 
rect, and  therefore  the  group.  But  from  what  has  been 
said,  it  will  be  seen  that  each  object  is  likely  to  be  a  little 
out  of  proportion,  indeed,  we  may  say,  is  sure  to  be  so. 
This  being  the  case  the  errors  are  multiplied,  and  if  the 
height  and  width  are  compared,  the  proportion  will  be 
found  to  be  far  from  correct.  It  is  a  principle  commonly 
acknowledged  now,  that  in  all  teaching  the  whole  should 
be  presented  before  its  parts,  so  that  it  cannot  be  contra- 
dicted that  adding  one  object  to  another,  until  finally  the 
patch-work  is  complete,  is  a  very  uneducational  way  of 
proceeding.  Practically  it  is  also  a  very  unsatisfactory 
one,  as  with  each  object  the  difficulties  increase,  and  at  last 
it  becomes  impossible  to  place  the  drawings  where   they 

(12) 


GROUPS.  13 

belong.  The  only  logical  way  is  to  draw  the  group  all  at 
once,  first  considering  it  as  a  mass  and  blocking  in  its  pro- 
portions by  straight  lines  passing  from  the  principal  points 
(see  Fig  5).  When  these  lines  have  been  drawn  and  con- 
sidered, they  may  be  tested  by  measuring  the  whole  height 
and  width,  and  the  directions  tested  by  use  of  the  thread 
or  pencil  as  explained. 

The  proportions  of  the  whole  being  thus  determined  as 
nearly  as  measurements  can  determine,  the  objects  may 
now  be  sketched  in  by  eye,  the  most  important  lines  being 
drawn  first ;  that  is,  the  lines  whose  positions  and  directions 
are  easiest  seen.  Such  lines  will  be  the  longest  lines,  and 
those  which  are  brought  out  distinctly  by  shade,  and  lines 
of  one  object  which  are  nearly  continuations  of  the  lines 
of  some  other  object.  It  is  evident  that  in  this  way  the 
drawings  of  the  objects  are  proceeding  at  the  same  time, 
and  the  shorter  and  less  prominent  lines  being  drawn  last, 
the  group  may  be  said  to  be  drawn  all  at  once. 

While  drawing,  the  student  must  think  of  the  tests 
applied  by  the  thread,  the  horizontal  and  vertical  lines,  and 
the  continuing  of  lines ;  and  the  drawing  in  the  air,  or  pass- 
ing of  the  pencil  point  over  the  edge  to  be  represented,  will 
help  greatly.  The  objects  should  be  studied  in  this  way, 
and  changed  as  often  as  found  incorrect,  until  no  further 
changes  can  be  made.  It  is  now  time  to  apply  systemati- 
cally the  tests  as  explained  in  the  drawing  of  the   box, 

Fig.  1. 

The  first  test  is  to  measure  the  height  and  width  of  each 
single  object  of  the  group,  and  compare  the  same,  and  also 


14  GROUPS. 

to  compare  with  the  dimensions  of  -the  whole  group.     This 
test  is  the  most  important,  and  the  greatest  care  should  be 
taken  with  it.     The  best  way  will  be,  as  soon  as  the  propor- 
tions have  been  determined,  to  draw  horizontal  and  vertical 
lines,  forming  a   rectangle  enclosing  the  drawing,  and  to 
be '  careful  that   these   lines    are  not    removed.       As   we 
have   seen,  slight  inaccuracy  can  hardly  be  avoided,  but 
these  dimensions  are  the  longest  measurements,  and   can 
therefore  be  fixed  more  accurately  than  any  others.     This 
being  so,  the  best  that  can  be  done  is  to  make  the  drawing 
agree  with  these  measurements ;  and  by  this  time  the  stu- 
dent should  be  able  to  measure  with  the  pencil  or  needle 
as  accurately  as  any  drawings  will  require.     This  test  Avill 
generally  change  the  drawing  throughout,  which  should  be 
done  not  by  erasing  but  by  adding  lines,  and  without  other 
measurements,  until  the   eye   can   see   no   more   changes. 
Then  the  thread  may  be  used  for  the  tests  of  horizontal 
and  vertical  lines  first;  and  second,  the  continuing  of  all  the 
edges ;  and  third,  for  covering  points  in  the  group  opposite 
each  other,  and  chosen  at  random,  that  the  intersections 
with  the  edges  between  may  be  noted.     The  thread  used 
thus   will   discover    every   discrepancy   except    the   slight 
deviations  which  only  the  accurate  eye  can  detect.     After 
the  training  which  is  given  by  these  drawings  made  en- 
tirely by  eye  before  any  tests  are  applied,  this  accuracy 
will  soon  be  secured.     When  the  correct  lines  have  been 
found,  the  others  are  to  be  erased  as  explained  on  page  10, 
and  the  lining  in  is  to  be  done. 

But  now  the  student  will  do  well  to  think  of  effect,  and 


GROUPS.  15 

to  see  if  more  interest  and  expression  cannot  be  given  to 
the  drawing  than  is  done  by  the  even  outline.  The  student 
has,  perhaps,  been  taught  that  the  nearest  objects  are  seen 
most  strongly,  and  that  the  strength  diminishes  with  the 
distance,  and  this  is,  of  course,  true  in  a  general  way.  It 
is  the  effect  of  gerial  perspective,  or  the  changing  of  color 
by  the  intervening  atmosphere.  Thus,  of  a  row  of  light 
objects,  the  nearest  will  be  the  brightest,  that  is,  the  light- 
est and  most  prominent,  and  of  dark  objects  the  same  princi- 
ple is  true.  The  light  object  in  the  distance  appears  darker,* 
and  the  dark  one  lighter,  so  that  in  a  sketch  taking  in  any 
considerable  distance  this  principle  will  be  of  assistance. 
But  it  must  be  stated  so  as  not  to  convey  the  idea  that 
there  can  be  nothing  in  the  distance  which  is  stronger  than 
anything  in  the  foreground,  for  we  do  not  see  objects  more 
or  less  distinctly  according  to  their  distance.  Distance,  in 
fact,  has  practically  nothing  to  do  with  it.  We  distinguish 
objects  as  masses  of  color,  light  or  dark,  according  to  the 
color  against  ivhich  they  are  seen.  This  being  so,  it  will 
be  seen  that  a  light  object  in  the  background,  as  a  white 
house,  seen  against  dark  foliage,  must  be  a  much  more 
prominent  feature  of  a  landscape  than  a  near  object  which 
is  seen  against  another  of  the  same  value.  In  general,  when 
there  is  little  or  no  contrast  of  color  between  objects,  then 
are  they  difficult  to  see  without  regard  to  their  distance. 

Place  a  square  of  white  cardboard  centrally  in  front  of  a 
larger  square  of  the  same,  the  latter  coming  in  front  of  the 

•Very  light  objects  may  change  but  little. 


16  GROUPS. 

blackboard.  The  smaller  can  be  seen  very  faintly,  but  in 
comparison  with  the  distinctness  with  which  the  larger  is 
seen  against  the  blackboard  the  nearer  plane  is  practically 
invisible.  This  experiment  proves  that  we  see  objects  to 
distinguish  their  form,  through  contrasts  of  color,  and  we 
have  to  consider  what  can  be  done  in  outline  simply  to 
render  the  effect  of  nature,  for  it  is  reasonable  to  expect 
from  every  medium  its  full  possibilities.  Can  no  more  be 
done  than  to  represent  the  outlines  in  an  even  line  ?  The 
opinion  seems  to  be  general  that  more  can  be  done.  We 
find  that  instructions  are  often  given  to  shade  the  nearer 
lines  strong,  the  further  ones  light,  and  to  grade  the  others 
between  them.  Apply  the  rule  to  the  representation  of 
the  two  planes  of  cardboard,  and  the  nearer  is  lined  in 
heavily  and  the  further  lightly.  This  we  find  to  be  in 
direct  contradiction  to  the  way  we  see  the  two  objects,  for 
the  nearer  is  barely  seen  against  the  further  white,  while  the 
more  distant  is  distinct  against  the  blackboard.  In  color  we 
certainly  should  not  think  of  representing  the  nearer  darker 
than  the  further,  or  in  any  other  Avay  than  as  it  appears, 
and  the  same  is  true  of  light  and  shade.  Why  should  we 
not  do  the  same  with  outline  ?  No  reason  to  the  contrary 
can  be  given,  for  the  difference  in  clearness  with  which  the 
various  lines  are  seen  is  the  result,  not  of  distance,  but  of 
contrast  of  light  and  shade.  Of  course  we  shall  expect  to 
find  the  strongest  line  among  the  nearer  ones,  but  further 
than  this  we  cannot  go,  and  if  we  adopt  the  conventional 
lining  in  often  recommended,  we  are  working  by  rule  and 


GROUPS.  17 

not  by  observation,  and  the  result  will  be  the  production  of 
hard,  mechanical  drawings. 

Character  appears  in  the  outlines.  An  object,  as  a  cast, 
having  a  smooth,  hard  surface,  and  an  eren  outline  shows 
these  qualities  in  its  outlines.  They  will  be  represented  by 
smooth  and  even  lines.  A  cube  with  smooth  faces  has; 
sharp'straight  edges,  which  must  be  represented  by  straight 
lines.  A  box  made  of  rough  boards  will  have  broken 
edges,  and  their  character  will  be  given  by  drawing  the 
irregular  outline  in  which  one  surface  cuts  into  the 
other.  A  drawing  from  the  figure  can  express  the  varia- 
tions in  the  appearance  of  the  outlines,  some  parts  of  which 
are  sharp,  some  parts  blurred  by  light  showing  through, 
or  by  a  short  growth  of  hair.  The  influence  of  light  also 
affects  the  appearance  of  the  outlines,  in  some  places  making 
them  distinct,  in  other  places  indistinct.  An  even  outline 
for  everything  disregards  all  these  variations  of  effect,  so 
also  does  any  conventional  variation  of  strength.  If  the 
student  is  allowed  to  disregard  effects  in  outline  work,  he 
will  have  very  great  difficulty  in  seeing  them  in  his  later 
work.  There  is  no  more  labor  involved  in  representing  the 
effects  than  in  disregarding  them,  for  one  line  is  as  easy  to 
make  as  another,  observation  only  being  required.  The 
student  who  can  see  can  perform,  and  as  long  as  any  differ- 
ences can  be  found  between  his  drawing  and  nature  he  can 
learn  to  correct  the  errors. 

In  pencil,  as  in  the  other  mediums,  we  should  do  the  best 
we  can  to  express  what  is  before  us,  and  the  effect  of  the 
drawing  should  be  considered  as  well  as  the  forms  repre- 


18  ■        GROUPS. 

sented.     There  is  no  reason  wliy  the  student  should  not  be 
taught  to  observe  the  effect,  and  if  once  started  correctly 
he  will  advance  rapidly,  and  will  make  drawings  which, 
since  they  are  representations  of  nature,  will  have  variety 
of  effect,  will  be  true,  and  thus  artistic.     Xo  rule  can  be 
given  other  than  to  study  and  represent  simply  what  is 
seen,  as  far  as  possible  as  it  appears.     In  outline,  without 
light  and  shade,  it  is  impossible  to  draw  always  just  what 
is  seen.     For  instance,  some  edges  of  the  object  may  be  so 
lost  in  the  shade  as  to  be  entirely  invisible,  but  without 
them  the  drawing  would  be  incomplete  and  unsatisfactory. 
A  correct  impression  of  the  facts  must  he  conveyed.      No 
important  line,  even  though  it  be  lost  in  shadow,  can  be 
omitted,  but  otherwise  the  lines  should  be  represented  just 
as  they  are  seen.     At  first  most  students  will  have  great 
difficulty  in  finding  that  there  is  any  difference  in  the  way 
in  which  the  various  edges  appear.     This  is  due  to  the  fact 
that  but  a  single  point  can  be  clearly  seen  at  any  one  time. 
The  eye  passes  rapidly  over  the  whole  extent  of  an  object, 
so  that  it  is  all  carefully  observed,  but  we  are  unconscious 
of  this  motion.     All  parts  of  the  object  are  seen  distinctly, 
and  the  variety  in  the  effect  is  not  realized,  and  all  points 
will  continue  to  give  the  impression  of  equal  strength  in 
the  effect,  until  the  ability  to  see  the  whole  of  an  object  at 
once  has  been  acquired.     It  is  not  possible,  otherwise,  to  see 
simply  and  broadly,  to  realize  effects  and  masses,  and  the 
student  must  practise  until  he  can  thus  see  before  he  thinks 
of  success  in  any  medium,  for  all  demand  equally  a  study 
of  the  comparative  strength  of  detail. 


GROUPS.  19 

The  whole  of  an  object  of  any  size,  or  the  effect  of  a 
group,  can  only  be  seen  when  the  vision  is  blurred  so  that 
all  parts  are  seen  equally  and  necessarily  indistinctly. 
This  effect  conies  from  looking  with  the  eyes  in  focus  for  a 
shorter  or  longer  distance,  and  is  the  same  as  that  given 
by  looking  through  a  lens  of  ten  or  twelve  inch  focus. 
Opening  the  eyes  and  looking  intently  until  the  vision  is 
blurred,  is  better  than  nearly  closing  them,  for  this  cuts 
off  most  of  the  light  and  loses  the  color.  In  light  and 
shade  this  point  would  not  do  harm,  but  it  is  better  to 
study  in  light  and  shade  so  as  not  to  be  obliged  to  change 
for  the  more  advanced  work.  After  a  little  practise  the 
student  will  be  able  to  see  the  whole  of  the  object  without 
special  effort,  and  it  must  not  be  forgotten  that  this  is  the 
only  way  in  which  effects  can  be  seen. 

Although  no  rule  for  lining  in  can  be  given,  the  effect 
will  always  be  found  to  conform  to  the  principle  that  any 
detail  tvhich  comes  in  either  the  mass  of  the  light  or  the 
mass  of  the  shade  is  unimportant,  that  is,  a  light  surface 
against  a  surface  also  light  is  not  prominent,  and  an  edge 
defining  a  surface  which  is  in  the  shade  against  another 
surface,  also  in  shade,  is  seen  faintly.  The  important  fea- 
tures, or  the  lines  which  are  prominent,  are  those  which 
come  between  the  light  and  shade. 


PERSPECTIVE    PRINCIPLES. 

Before  beginning  we  will  choose  a  term  which  shall  mean 
the  position  in  which  any  line  appears  of  its  real  length, 
and  any  plane  of  its  real  shape.  This  will  occur  when  the 
line  or  the  plane  is  perpendicular  to  the  direction  in  which 
it  is  seen,  that  is,  is  parallel  to  the  picture  plane.  The 
words  parallel  to  the  picture  plane  might  cause  confusion, 
from  the  fact  that  in  perspective  the  picture  plane  is  gener- 
ally vertical,  and  often  takes  in  a  wide  field  of  view,  while 
in  moael  drawing  the  plane  is  perpendicular  to  the  direc- 
tion in  which  one  looks,  and  is  thus  continually  changing. 
We  wish  a  term  which  shall  mean  any  position  in  which 
any  line  or  plane  appears  of  its  real  shape,  and  will 
select  the  phrase,  "  directly  in  front."  Any  line  is  directhj 
in  front  when  its  ends  are  equally  distant,  and  any  rectan- 
gular plane  when  its  angles  are  equally  distant  from  the  eye. 

Place  a  large  cube  horizontal,  with  its  centre  on  a  level 
with  the  eye,  the  cube  being  a  few  feet  distant.  The  front 
face  directly  in  front,  with  its  four  corners  equally  distant, 
appears  of  its  real  shape  (Fig.  6).  Now  turn  the  cube  so 
that  its  left  side  is  seen  very  narrow  (Fig.  7).  It  will  be 
noticed  that  the  upper  end  of  the  vertical  edge,  B,  at  the 
back  appears  beloAv,  and  the  lower  end  appears  above  the 
respective  ends  of  the  front  vertical  edge,  A.  In  other 
words,  the  further  edge  appears  shorter  than  the  front,  and 
the  horizontal  edges,  D,  E,  connecting  their  extremities, 
must  appear  to  converge,  and  if  continued  would  meet.  From 

(20) 


PERSPECTIVE  PRINCIPLES.  21 

this  we  see  :  First — That  of  two  parallel  and  equal  edges,  the 
nearer  appears  the  longer,  the  relative  lengths  being  in- 
versely as  the  distances.     See  Fig.  8,  in  which  B,  being  twice 
the  distance  of  A,  appears  one-half  its  length.     Second — 
That  parallel  retreating  edges   {all  not   directly   in  front) 
appear  to  converge  or  vanish  at  a  point  called  their  vanishing 
point.     Third — That  horizontal  edges  above  the  eye  appear 
in  retreating  to  descend  or  vanish  doivnward,  while  those 
beloiv  the  eye  in  retreating  appear  to  ascend  or  vanish  iip- 
ward.         This  is  easily  proved  by  the  fact  that  the  eye 
must  be  dropped  in  looking  from  a  nearer  to  a  farther  point 
in  the  edge  above  the  eye,  and  raised  for  the  more  distant 
point  in  the  line  below  the  eye.     Lift  the  eye  to  the  level 
of  the  top  of  the  cube  and  it  will  appear  a  horizontal  line, 
thus  showing  that  a  horizontal  line  at  the  level  of  the  eye 
appears  horizontal,  and  that  a  plane  so  situated  is  seen  edge- 
wise and  appears  a  horizontal  line,     l^ow  place  the  eye  in 
the  first  position,  on  a  level  with  the  centre  of  the  cube. 
The  right  hand  vertical  edge,  C,  is  farther  from  the  eye 
than  the  central  edge,  A.     It  must  therefore  appear  shorter, 
and  the  horizontal  edges,  F  and  G,  must  converge  as  those 
at  the  left.     If  both  these  sets  of  edges  are  continued  they 
will  appear  to  meet  at  two  vanishing  points,  and  since  the 
edges  are  equally  above  and  below  the  eye,  the  upper  and 
lower  angles  of  convergence  1-2  and  3-4  must  be  equal  on 
each  side  of  A,  and  the  vanishing  points  be  on  a  level  with 
the  centre  of  the  cube,  that  is,  of  the  eye.     Hence,  we  sse 
that  parallel  horizontal  edges  appear  to  vanish  at  the  level 
of  the  eye.     We  will  now  draw  upon  the  end  of  a  room, 


22  PERSPECTIVE  PRINCIPLES. 

Fig.  9,  lines  which  continue  the  apparent  directions  of  the 
horizontal  edges  at  floor  and  ceiling,  which  are  perpendi- 
cular to  the  end.  We  find  them  to  intersect  at  a  point 
which  is  directly  opposite  the  eye.  This  point  on  the  wall 
being  the  picture  of  the  infinitely  distant  point  in  which 
the  continued  lines  seem  to  meet,  and  the  line  from  this 
point  to  the  eye  being  parallel  to  the  lines  A,  B,  C,  D,  we 
see  that  the  vanishing  poiiit  of  any  set  of  parallel  lines  is 
in  a  line  parallel  to  them  passing  through  the  eye.  To  draw 
these  lines  on  the  wall  two  students  must  work  together, 
but  the  directions  can  be  determined  with  a  straight  edge, 
and  the  students  may  work  individually  by  drawing  the 
interior  of  any  room.  This  experiment  is  the  best  way  to 
show  that  to  find  the  vanishirig  ^Joint  of  lines  we  must  look 
in  their  direction. 

All  parallel  edges  which  have  one  end  nearer  the  eye  than 
the  other  must  appjear  to  converge,  and  the  convergence  must 
he  in  the  direction  of  their  farther  ends.  According  to  this 
statement,  when  the  cube  is  above  or  below  the  eye  its 
vertical  edges  must  vanish.  The  edges  do  appear  to  vanish, 
but  they  are  not  so  represented.  In  a  model  dratoing,  verti- 
cal edges  are  represented  hy  vertical  lines. 

Place  a  small  cube  so  that  its  top  and  front  faces  are  seen, 
and  its  right  side  is  seen  as  a  vertical  line  (Fig.  10).  The 
edges,  A,  A,  A,  are  so  nearly  directly  in  front  that  they  may 
be  represented  by  parallel  horizontal  lines.  Line  B  of  the 
drawing  will  be  found  to  be  longer  than  line  C,  and  yet  C 
is  nearer  the  eye.  We  see  that  the  first  statement  illus- 
trated by  Fig.  8  must  be  qualified.     A  study  of  Fig.  11  will 


PERSPECTIVE    PRINCIPLES.  23 

show  that  of  two  parallel  and  equal  lines  unequally  distant 
from  the  eye,  the  nearer  A-B  appears  the  shorter  when  its 
angle  with  the  plane  of  the  picture  is  greater  than  forty-five 
degrees^  and  that  of  two  lines,  B-D  and  A-C,  the  nearer  B- 
D  appears  the  longer  when  the  angle  of  the  lines  with  the  pic- 
ture is  less  than  forty-five  degrees.  This  statement  may  not 
be  exact  for  lines  whose  angle  is  very  nearly  forty-five 
degrees,  but  when  there  is  a  noticeable  difference  it  is  cor- 
rect. The  figure  also  shows  that  of  two  equal  lines,  A-B  and 
B-D,  perpendicular  to  each  other  and  having  one  end  com- 
mon, the  one  which  makes  the  greatest  angle  with  the  pic- 
ture appears  the  shorter.  That  which  is  nearest  parallel 
appears  the  longer. 

Fig.  12  shows  that  two  lines  perpendicidar  to  each  other, 
at  equal  angles  with  the  picture  and  having  their  ends 
equally  distant,  appear  of  equal  length.  The  statement 
often  found  that  of  parallel  and  equal  lines  the  more  dis- 
tant appears  the  shorter,  has  accomplished  perhaps  as  much 
harm  as  good,  for  it  is  only  correct  for  lines  directly  in  front 
and  for  vertical  lines. 

In  Fig.  13  line  A-B  represents  the  ground,  and  points 
1,  2,  3,  etc.,  equi-distant  points  situated  in  a  line  lying  on 
the  ground.  The  lines  drawn  from  these  points  to  the  eye 
represent  the  rays  in  which  the  points  are  seen,  and  the 
intersections  of  the  rays  with  the  picture  plane  show  that 
the  equal  distances  appear  unequal,  the  nearest  appearing 
the  longest,  the  furthest  the  shortest,  and  the  intermediate 
distances  proportional  between  these  lengths,  and  this  is 
always  true  of  equal  spaces  on  any  retreating  line. 


24  PERSPECTIVE  PRINCIPLES. 

It  will  be  seen  that  there  are  three  sets  of  parallel  edges  in 
the  cube,  and  that  they  all  appear  to'vanish,  unless  directly 
in  front,  and  are  so  represented  unless  they  are  vertical,  or 
situated  as  in  Figs.  10  and  14.  They  vanish  in  the  direction 
of  their  farther  ends,  and  these  points  are  angles  of  the 
invisible  faces  of  the  solid.  If  both  ends  of  a  line  answer 
this  condition,  the  line  must  be  considered  as  directly  in 
front,  even  if  the  eye  is  not  exactly  opposite  its  centre. 
In  general,  parallel  straight  lines  which  extend  on  both  sides 
of  the  spectator  must  be  represented  by  parallel  straight 
lines.  If  the  eye  should  be  opposite  one  end  as  in  Tig.  10, 
and  the  edges  are  short,  they  will  be  best  represented  by 
parallel  horizontal  lines.  If  the  edges  are  long  and  near 
the  spectator,  it  may  sometimes  be  better  to  distort  the 
nearer  and  smaller  part  of  the  object  in  favor  of  the  farther 
and  larger  part,  by  drawing  the  more  distant  end  smaller 
than  the  nearer  Fig.  14.  This,  however,  will  seldom  hap- 
pen, and  unless  special  permission  to  the  contrary  is  given, 
the  edges  are  to  be  treated  as  if  directly  in  front  until  a  side 
face  is  seen. 

In  nature  there  is  no  so-called  parallel  or  one-point  per- 
spective, that  is,  parallel  perspective  is  not  true  to  appear- 
ances. It  therefore  should  be  avoided,  and  the  difficulties 
which  have  just  been  considered  will  be  best  settled  by 
moving  so  that  the  edge  is  directly  in  front,  or  so  that  a 
side  face  is  seen  and  there  are  two  vanishing  points.  When, 
however,  this  cannot  be  done,  and  parallel  straight  lines 
extend  on  both  sides  of  the  spectator,  the  student  must 
represent  them  by  straight  lines,  and  in  the  case  of  hori- 


PERSPECTIVE  PRINCIPLES.  25 

/ 

zontal  edges  by  horizontal  lines.  Long  parallel  straight 
lines  in  nature  appear  curved.  This  is  shown  in  the  shadows 
of  clouds  at  sunset,  which  sometimes  may  be  seen  extend- 
ing across  the  sky,  and  converging  in  the  east  and  west. 
In  many  drawings  from  nature  of  streets,  etc.,  by  our  best 
illustrators,  the  curvature  is  so  marked  that  it  is  most 
noticeable.  The  representation  of  straight  by  curved  lines 
should  not  be  allowed  the  student,  and,  as  shown  on  page 
72,  straight  lines  may  be  substituted  for  the  curved,  chang- 
ing the  drawing  but  little  when  there  are  two  vanishing 
points.  When  the  end  of  a  room  is  shown  certainly  no  one 
would  wish  to  represent  the  curvature,  for  the  drawing  should 
give  the  impression  of  nature,  and  this  can  only  be  done  by 
straight  lines. 


'■0-' 


THE   CUBE. 

These  principles  are  illustrated  by  the  cube  (of  four-foot 
edge,  scale  ^  in.  =  1  ft.)  drawn  in  various  positions  : 

First.  The  cube  with  four  edges  vertical,  its  under  sur- 
face being  on  the  level  of  the  eye,  one  surface  only  visible, 
and  the  eye  being  opposite  the  centre  of  edge  A-B.  The 
under  surface  must  appear  a  horizontal  line.  The  front 
surface,  although  its  upper  angles  are  further  from  the  eye 
than  the  lower,  will,  unless  the  eye  is  very  near  the  object, 
appear  practically  of  its  real  shape  (Fig.  15). 

Second.  Lower  the  cube  until  its  top  is  four  feet  below 
the  level  of  the  eye  (Fig.  16).  The  receding  edges  of  the 
top  will  vanish  in  a  point  on  the  level  of  the  eye,  and  in  a 
line  drawn  through  the  eye  parallel  to  the  edges.     This 


26  PERSPECTIVE  PRINCIPLES. 

places  the  point  above  the  centre  of  the  cube.  The  front 
face  being  below  the  eye  will  be  foreshortened  (as  shown 
by  Fig.  17),  so  that  it  will  not  appear  of  its  real  shape. 
The  edge,  E-F,  being  further  from  the  eye  than  A-B,  will 
appear  shorter,  just  as  C-D  does.  It  will  appear  the  length 
of  1-2,  and  the  vertical  edges,  by  connecting  points  A-1  and 
B-2,  will  be  represented  by  inclined  lines.  The  representa- 
tion of  vertical  by  inclined  lines  is  not  satisfactory,  and  the 
model  drawing  must  have  vertical  lines.  If  the  lines  are 
drawn  vertical  from  A  and  B,  the  front  face  will  seem  too 
wide  ;  if  from  1  and  2,  it  will  be  too  narrow.  The  proper 
effect  will  be  given  by  verticals  midway  between,  or  if  they 
are  drawn  from  A  and  B,  the  line  1-2  must  be  dropped  to 
give  the  correct  impression.  It  will  be  seen  that  the  model 
drawing  is  not  the  exact  drawing  upon  the  inclined  picture 
plane,  but  this  drawing  corrected  by  substituting  vertical 
for  inclined  lines.  When  edges  are  situated  on  each  side 
of  the  eye,  as  are  A-C  and  B-D,  they  must  always  appear  to 
vanish  at  a  point  which  is  directly  opposite  the  eye,  for  the 
vanishing  point  of  a  line  is  in  a  parallel  to  the  line  passing 
through  the  eye. 

Third.  Place  the  cube  with  its  vertical  faces  at  forty- 
five  degrees  to  the  picture  plane,  its  top  being  on  a  level 
with  the  eye  (Fig.  18).  The  top  is  seen  edgewise.  The 
sides,  since  at  equal  angles,  will  appear  of  equal  width. 
The  edges,  A  and  B,  must  vanish  upward  at  equal  angles, 
the  angle  depending  wholly  on  the  distance  of  the  eye.  If 
short,  the  convergence  will  be  rapid,  and  the  angle  of  con- 
vergence will  decrease  as  the  distance  increases. 


PERSPECTIVE    PRINCIPLES.  27 

Fourth.  The  cube,  with  its  lower  surface  on  the  level  of 
the  eye,  and  its  vertical  faces  at  angles  of  thirty  degrees  to 
left  and  sixty  degrees  to  right  (Fig.  19).  The  left  face, 
being  nearest  parallel  to  the  picture  plane,  appears  the 
Avider.  The  edges,  A  and  B,  vanish  downward  at  angles 
Avhich  depend  on  the  distance  of  the  eye,  but  that  of  A  must 
always  be  less  than  that  of  B. 

Fifth.  The  cube,  with  its  top  four  feet  below  the  eye, 
and  its  sides  at  forty -five  degrees  (Fig.  20).  The  sides  must 
appear  of  equal  width,  and  the  angles  of  the  lines  on  each 
side  be  equal.  There  are  four  parallel  edges  extending  to 
the  right,  and  four  to  the  left.  Parallel  lines  appear  to 
converge  at  a  point,  and  for  horizontal  lines  this  point  is  at 
the  level  of  the  eye.  The  two  vanishing  points  will  then 
be  on  the  level  of  the  eye,  and  must  be  equi-distant  from 
the  drawing.  This  distance  depends  on  the  distance  of  the 
eye,  increasing  equally  with  it.  (For  an  angle  of  forty-five 
degrees  the  distance  of  the  vanishing  point  is  equal  to  that 
of  the  eye.)  In  this  position  of  the  square,  which  is  the 
base  of  the  cube,  it  will  be  seen  that  one  diagonal  of  the 
base  is  parallel  to  the  picture  plane,  and  appears  a  horizontal 
line.  The  other  diagonal  appears  a  vertical  line,  and 
the  further  angle  of  the  square  is  directly  over  the  nearer 
one. 

Sixth.  The  cube  above  the  eye,  with  its  horizontal  edges 
extending  to  left,  at  sixty  degrees,  and  to  right  at  thirty 
degrees  (Fig.  21).  Both  sets  of  lines  will  vanish  at  points 
in  the  horizon,  the  vanishing  point  at  the  left  being  the 
nearest  to  the  drawing,  for  the  line  at  the  greatest  angle 


28  PERSPECTIVE  PRINCIPLES. 

must  appear  the  shortest.  The  diagonals  of  the  horizontal 
surface  will  also  vanish.  Of  the  diagonal  1-2,  2  is  the 
nearest  point,  and  the  line  must  vanish  to  the  left.  Point 
3  is  the  nearest  end  of  3-4,  and  this  line  vanishes  to  the 
right. 

Seventh.  The  cube,  resting  on  an  edge  on  the  ground, 
four  of  its  faces  being  at  forty-five  degrees  to  the  ground, 
being  seen  from  above,  and  having  three  faces  visible 
(Fig.  22).  Let  line  1-2  be  the  edge  on  the  ground.  For  four 
faces  to  be  at  forty-five  degrees  to  the  ground,  it  is  neces- 
sary that  the  diagonals  of  the  two  faces  which  are  vertical, 
shall  be  vertical  and  horizontal.  Vertical  lines  from  1  and 
2  must  be  the  vertical  diagonals.  The  horizontal  diagonals, 
34  and  5-6,  must  bisect  the  vertical  and  vanish  in  the  hori- 
zon. The  edges  parallel  to  1-2  vanish  at  the  left,  at  the 
level  of  the  eye.  From  point  3  an  edge  extends  downward, 
and  another  upward.  The  lines  which  are  parallel  must 
vanish  respectively  up  and  down  to  the  right. 

These  principles  will  enable  one  not  only  to  correct  or 
test  drawings  made  from  the  object,  but  what  is  more  im- 
portant, to  design  or  draw  without  the  objects.  Thus,  let 
line  A,  Fig  23,  be  the  nearest  edge  of  a  cube,  situated 
below  the  eye,  with  its  faces  at  such  angles  that  the  width 
on  each  side  extends  to  B  and  C.  Drawing  a  horizontal 
through  the  end  of  A  we  know  that  the  edge  extending 
to  the  right  must  make  a  greater  angle  than  that  going  to 
the  left.  Such  practice  will  enable  one  to  draw  quite 
correctly  without  the  objects. 


TERSPECTIVE  PRINCIPLES.  29 

THE    SQUARE    PYRAMID. 

When  the  pyramid  stands  on  its  base,  its  axis  being  ver- 
tical, is  drawn  by  erecting  a  vertical  at  the  intersection  of 
the  diagonals  of  the  square.  When  two  sides  of  the  base 
are  directly  in  front  (Eig.  24),  one  side  only  of  the  pyra- 
mid will  be  seen  if  its  axis  is  long,  or  if  it  is  above  the  eye. 
If  its  axis  is  short  or  wholly  below  the  eye,  two  side  faces 
may  be  seen,  and  will  appear  equally  (Fig.  25).  When  two 
faces  are  seen  all  the  edges  of  the  base  must  vanish.  When 
two  faces  are  seen  alike,  the  edges  of  the  base  are  at  equal 
angles  with  the  picture  plane.  The  slant  edges  at  front 
and  back  appear  to  coincide,  and  one  diagonal  of  the  base 
is  horizontal  (Fig.  26). 

When  two  faces  of  the  base  are  seen  unequally  (Fig.  27), 
the  axis  of  the  pyramid  will  be  perpendicular  to  a  line 
which  is  parallel  to  the  picture  plane.  A  plan  view  of  the 
square  and  the  P.  PI,  will  show  the  position  of  the  line  a-b 
with  reference  to  points  1  and  2  of  the  square.  This  line 
must  pass  behind  point  2  (which  point  is  nearer  the  eye  than 
point  1),  and  in  front  of  point  1.  When  the  pyramid  is 
vertical  line  a-b  will  be  horizontal.  When  the  pyramid  is 
oblique  (Fig.  28)  the  line  may  be  a  test,  but  not  sufficiently 
accurate  to  be  of  value  except  when  drawing  without  the 
object. 

THE   TRIANGLE   AND  PRISM. 

When  this  figure  is  equilateral  or  isosceles,  and  rests  on 
a  base,  the  altitude  is  vertical,  and  intersects  the  centre  of 
the  base  (Fig.  29). 


30  PERSPECTIVE  PRINCIPLES. 

The  prism  with  equilateral  ends,  resting  on  a  face  on  the 
ground. 

First  (Fig.  30).  When  neither  end  is  seen,  the  long 
edges  are  directly  in  front,  and  must  be  represented  by 
parallel  lines.  When  one  end  is  seen,  and  two  sides  equally 
(Fig.  31),  the  edge  A  of  the  end  is  directly  in  front.  When 
an  end  and  a  side  are  seen  (Fig.  32),  the  end  will  be  tested 
by  a  vertical  through  point  1.  This  should  come  at  point  4. 
the  centre  of  the  base  2-3,  but  4  does  not  bisect  the  line  2-3, 
as  the  nearer  half  must  perspectively  appear  longer  than 
the  further  half.  The  edges  must  vanish  in  the  direction 
of  their  farther  ends.  This  direction  is  at  once  apparent, 
except  in  the  case  of  1-2,  whose  direction  will  be  deter- 
mined by  seeing  which  point,  1  or  2,  is  nearest  to  the  line 
3-7.  The  point  which  is  nearest  is  the  nearest  end  of  the 
line  1-2.  Suppose  the  prism  placed  so  that  the  edges  of 
the  face  on  the  ground  are  at  equal  angles  with  the  picture 
plane.  They  will  vanish  equally,  and  the  line  2-3  will  be 
equal  to  one-half  of  2-6,  the  nearer  half  perspectively  ap- 
pearing a  little  longer  than  the  further  half. 

THE  EEGULAR   HEXAGOX   AXD   SOLIDS. 

In  the  hexagon  there  are  four  sets  of  parallel  lines.  A,  B,  C, 
and  D.  The  diagonal  0-4  is  divided  into  four  equal  parts 
by  the  diameters  D,  D,  and  the  diagonals  B-C.  A  model 
drawing  of  the  figure  may  be  tested  by  seeing  that  the 
parallel  edges  vanish  in  the  direction  of  their  further  ends, 
and  that  the  diameters  divide  the  diagonal  into  four  per- 
spectivelij  equal  parts. 


PERSPECTIVE  PRIXCIPLES.  31 

In  Fig.  33  the  hexagon  is  shown  directly  in  front.  In 
Fig.  34  it  is  shown  after  it  has  been  revolved  back  about 
the  angle  0.  Figs.  35  and  36  are  the  same,  the  hexagon 
being  revolved  about  the  side  A.  In  Figs.  34  and  36  the 
lines  a-a  may  be  drawn,  thus  enclosing  the  hexagon  by  a 
rectangle.  The  intersection  of  the  diagonals  of  any  rec- 
tangle gives  its  centre!.  By  drawing  them  in  these  figures 
and  lines  b,  the  angles  of  Fig.  34  are  determined.  In  Fig. 
33,  to  get  points  1  and  3,  it  is  only  necessary  to  divide  by 
diagonals  each  half. 

To  draw  the  hexagon  on  a  given  line,  a-b,  as  diameter 
(Fig.  37).  Draw  the  sides  A  and  B,  then  the  further  dia- 
meter c-d.  Draw  the  diagonals,  and  make  the  distance  4-5 
less  than  3-4,  and  1-2  greater  than  2-3. 

To  draw  a  hexagon  on  a  given  side,  A-B  (Fig.  38).  Draw 
the  diameters  from  A  and  B,  and  draw  the  further  side, 
C-D.  Draw  the  diagonals  A-D  and  B-C,  and  the  diagonal 
through  3.  If  A-B  and  C-D  are  directly  in  front,  1,  2,  3,  4 
and  5  will  be  equi-distant  points.  If  not  directly  in  front, 
the  points  will  be  perspectively  equi-distant. 

In  the  prism  and  pyramid,  Figs.  39,  40,  41  and  42,  no 
more  than  three  of  their  side  faces  and  an  end  can  be  seen 
at  any  time.  If  two  only  are  seen,  the  diameters  of  the 
base  are  directly  in  front.  When  three  are  seen,  and  the 
outer  ones  appear  of  equal  width,  the  ends  of  the  middle 
face  are  directly  in  front.  When  the  outer  faces  are  seen 
unequally,  the  narrower,  A  (Fig.  39),  must  be  the  more 
distant,  and  this  shows  the  direction  in  which  the  edges, 
a-b  and  c-d,  of  the  middle  face  vanish.     The  vanishing  of 


32  PERSPECTIVE  PRINCIPLES. 

the  parallel  edges  must  make  the  invisible  end  wider  than 
the  visible,  as  in  the  cylinder  (page- 35).  The  tests  for  the 
pyramid  are  the  same  as  for  the  prism  and  the  square 
pyramid.  When  three  faces  are  seen  and  the  outer  ones 
equally,  the  axis  is  perpendicular  to  the  longest  diagonal. 
When  two  are  seen  equally,  it  is  perpendicular  to  the  diam- 
eter. When  two  or  three  are  seen  unequally  it  is  perpen- 
dicular to  a  line  between  the  diameter  and  the  diagonal.  The 
faces  visible  will  show  whether  this  line  is  nearest  parallel 
to  the  diagonal  or  to  the  diameter.  In  Fig.  40  the  question 
may  arise,  "  Shall  the  nearer  half,  a-c,  of  the  diameter,  a-b, 
be  a  little  longer  than  the  further  part,  c-b  ?  "  It  will  be  seen 
that  doing  away  with  the  convergence  of  the  vertical  lines 
makes  the  equal  distances  a-c  and  c-b  equal  in  the  drawing. 

THE    CIRCLE. 

The  circle  appears  of  its  real  shape  when  directly  in 
front.  It  appears  as  a  straight  line  when  the  eye  is  in  its 
plane,  and  in  other  positions  in  which  its  entire  circumfer- 
ence is  seen,  it  appears  as  an  ellipse. 

Fig.  43  represents  a  square,  two  sides  being  directly  in 
front.  A  circle  inscribed  in  the  square  will  be  represented 
by  an  ellipse,  which  is  tangent  to  the  sides  of  the  square,  at 
the  ends  of  the  diameters  of  the  square,  in  points  1,  2,  3 
and  4.  The  centre  of  the  square  must  perspectively  come 
nearer  the  further  side,  C-D,  and  it  is  at  once  seen  that  the 
centre  of  the  circle  is  not  the  centre  of  the  ellipse,  that  is,  that 
the  long  axis  of  the  ellipse  is  not  a  diameter  of  the  circle. 
This  is  shown  again  by  Figs.  44  and  45. 


PEBSPECTIVE  PRIXCIPLES.  33 

Fig.  45  is  a  plan  view,  showing  the  circle,  the  eye,  and 
the  cone  of  rays  from  the  eye  to  the  circle, -represented  by 
its  outer  rays,  a-a.  Fig.  44  is  a  side  view,  showing  the 
ground,  B-D,  the  circle,  C-C,  the  eye,  and  the  cone  of  rays, 
b-b.  The  picture  plane,  at  right  angles  to  the  central  ray, 
A,  shows  the  width  of  the  ellipse  at  1-2.  The  central  ray 
intersects  the  ground  at  c,  and  this  must  be  the  position  of 
the  chord  34  of  the  circle  (seen  in  plan  view),  which  ap- 
pears the  long  axis  of  the  ellipse.  Points  3  and  4  are  not 
the  tangent  points  of  lines  a-a. 

All  lines  whose  ends  are  unequally  distant  must  vanish. 
It  follows  that  in  any  circle  there  can  be  but  one  diameter 
which  does  not  vanish.  This  must  be  the  one  which  is 
perpendicular  to  the  line  of  sight,  and  thus  directly  in 
front.  A  horizontal  line  directly  in  front  appears  horizon- 
tal, and  thus  a  horizontal  circle  must  appear  as  a  Itorizontal 
line,  or  as  a  horizontal  ellqise ;  for  though  the  diameter 
directly  in  front  is  not  the  long  axis  of  the  ellipse,  it  is  par- 
allel to  the  chord  of  the  circle  which  is  the  long  axis  of  the 
ellipse.  The  line  of  any  circle  which  is  the  long  axis  of  its  ap- 
pearance is  thus  a  chord  of  the  circle  which  is  directly  in  front. 

When  on  the  level  of  the  eye  the  horizontal  circle  ap- 
pears a  horizontal  line,  and  when  below  or  above  the  eye, 
an  ellipse,  whose  width  increases  with  the  distance  of  the 
circle  from  the  level  of  the  eye  (Fig.  46). 

The  short  axis  of  an  ellipse  is  perpendicular  to  its  long. 
It  represents  a  diameter  of  the  circle  which  is  perpendi- 
cular to  the  chord  which  appears  the  long  axis.  This  dia- 
meter will  be  found  to  appear  to  coincide  with  a  line  per- 


34  PERSPECTIVE    PRINCIPLES. 

penclicular  to  the  plane  of  the  circle  erected  at  the  centre 
of  the  circle.  Hence,  if  two  lines  are  perpendicular  to  each 
other,  one  is  directly  in  front,  and  the  other  intersects  the 
centre  of  the  first,  the  right  angles  thus  made  will  appear 
right  angles  until  the  second  line  is  seen  as  a  point. 

The  circle  when  vertical,  at  an  angle  with  the  picture, 
and  its  centre  on  the  level  of  the  eye,  will  appear  a  vertical 
ellipse.  When  the  vertical  circle  is  below  the  eye,  the  two 
equi-distant  points  in  its  circumference,  which  are  the  ends 
of  the  long  axis  of  the  ellipse,  must  be,  the  upper  point 
behind  the  highest  point  in  the  circle,  and  the  lower  point 
in  front  of  the  lowest  point.  The  chord  (that  is  the  long 
axis  of  the  ellipse)  connecting  these  points  must  be  an 
inclined  line.  When  the  circle  is  above  the  eye,  the  ends 
of  the  diameter  of  the  ellipse  will  be  in  front  of  the  highest 
and  behind  the  lowest  points  in  the  circle,  and  the  axis  of 
the  ellipse  will  incline  in  a  direction  opposite  from  that 
which  it  has  when  below  the  eye. 

The  axis  of  the  ellijjse  which  represents  a  vertical  circle 
on  any  level  except  that  of  the  eye,  must  he  an  inclined  line 
(Fig.  47).  In  this  figure  we  have  a  circle  A,  vertical,  and 
on  the  level  of  the  eye,  and  circles  B  and  C  of  the  same 
size,  directly  over  and  below  A,  and  in  the  same  plane.  It 
will  be  seen  that  the  ellipses  of  B  and  C  are  tangent  to 
verticals  tangent  to  A,  but  that  their  short  axes  are  shorter 
than  that  of  A.  To  determine  the  inclination  of  the  axis 
look  for  the  two  equi-distant  points  which  are  its  ends,  or 
look  for  the  direction  which  a  perpendicular  to  the  circle  at 
its  centre  would  have,  for  the  long  axis  is  perpendicular  to 


PERSPECTIVE    PRINCIPLES.  35 

this  direction.  The  latter  Avay  (which  is  the  better)  con- 
siders the  circle  the  base  of  a  cylinder  whose  direction 
determines  the  direction  of  its  end. 

THE    CYLINDER. 

Less  than  half  the  curved  surface  of  the  cylinder  can  be 
seen  at  any  one  time. 

Fig.  48.  When  an  end  only  is  seen,  it  must  appear  of  its 
real  shape.  When  neither  end  is  visible  (A),  the  cylinder 
must  be  directly  in  front,  both  ends  appearing  narrow  el- 
lipses. When  one  end  appears  a  straight  line  (B),  the  other 
must  appear  a  narrow  ellipse. 

The  long  axis  of  an  ellipse  appears  perpendicular  to  a 
line  which  is  perpendicular  to  the  circle  at  its  centre.  This 
line  in  the  cylinder  is  its  axis,  and  in  drawing  the  cylinder 
and  cone  the  long  axis  of  the  ellipse  of  the  base  must  always 
be  at  right  angles  to  the  axis  of  the  solid. 

When  the  surface  of  one  base  of  the  cylinder  is  visible, 
that  of  the  other  must  be  invisible.  The  visible  end  being 
nearest  the  eye,  the  invisible  must  appear  shorter,  and  the 
elements  connecting  them  must  converge  as  any  parallel 
straight  lines.  The  question  of  the  comparative  width  of 
the  visible  and  invisible  ends  has  caused  much  trouble.  A 
study  of  Figs.  11  and  12  will  show  this  width  to  be  depend- 
ent upon  the  position  of  the  cylinder.  When  it  is  at  a  less 
angle  than  forty-five  degrees  with  the  picture,  the  invisible 
base  will  be  the  wdder,  but  when  it  is  at  a  greater  angle 
than  forty-five  degrees,  the  invisible  base  will  be  the  nar- 
rower.    This,  however,  is  not  exact  for  angles  very  near 


36  PERSPECTIVE   PRINCIPLES. 

forty-five  degrees,  and  refers  to  positions  in  which  the 
object  is  at  a  sufficient  distance  to  permit  its  entire  repre- 
sentation. For  unusual  conditions,  as  a  very  long  object 
very  near  the  spectator,  or  for  a  number  of  objects  placed 
in  a  straight  line  and  extending  for  some  distance,  it  can- 
not apply,  as  the  distortion  caused  by  the  use  of  any  one 
picture  plane  would  be  very  great.  Such  conditions,  how- 
ever, are  not  normal,  and  it  is  best  not  to  attempt  to  draw 
an  object  which  is  so  near  as  to  create  a  visual  angle  of 
over  thirty  degrees.  The  invisible  base  is  always  at  a 
less  angle  to  the  plane  which  gives  its  real  appearance; 
that  is,  it  is  at  a  greater  angle  to  the  ray  from  the  eye  to 
its  centre  than  the  nearer  end  (Fig,  49),  and,  though  nar- 
rower than  the  visible  end  when  the  cylinder  is  at  a  greater 
angle  than  forty-five  degrees,  is  also  shorter,  and  is  always 
proportionally  voider  than  the  visible  end.  This  is  the  only 
rule  that  can  be  given,  the  difference  depending  upon  the 
distance  of  the  eye,  and  decreasing  as  this  distance  increases. 
When  this  distance  is  short  it  is  quite  marked. 

Figs.  50,  51,  52,  53,  54  and  55  show  the  cylinder  in 
various  positions,  and  all  illustrate  this  principle.  In  these 
drawings,  the  length  of  the  cylinder  is  supposed  to  be  twice 
its  diameter.  In  Fig.  50  the  cylinder  is  horizontal,  on  the 
level  of  the  eye,  and  extends  to  left  at  forty-five  degrees  to 
the  picture  plane.  The  short  axis  of  the  visible  end  must 
be  perspectively  one-half  of  the  element  a-b.  In  Fig.  51 
the  cylinder  is  at  an  angle  with  the  ground,  and  still  at 
forty-five  degrees  to  the  picture  plane,  the  appearance  being 
the  same  as  Fig.  50.     Figs.  53  and  54  show  two  cylinders, 


rEKSPECTIVE    PRINCIPLES.  37 

one  being  exactly  over  the  other.  In  Fig.  52  the  cylinder 
is  below  the  eye,  and  extends  directly  back.  The  tendency 
will  be  to  represent  the  ends  by  circles,  but  they  can  only 
so  appear  when  no  part  of  the  curved  surface  is  visible. 

THE    CONE. 

The  cone  appears  a  circle  when  its  axis  is  seen  as  a 
point ;  a  triangle  when  its  base  is  seen  as  a  line.  In  other 
positions  both  the  circle  and  the  curved  surface  will  be 
visible,  the  circle  appearing  an  ellipse.  The  curved  surface 
will  be  represented  by  the  two  contour  elements,  which 
must  be  tangent  to  the  ellipse  (Fig.  56).  The  entire  curved 
surface  will  be  visible  when  the  axis  is  toward  the  eye. 
When  the  cone  extends  in  the  opposite  direction  none  of 
the  curved  surface  will  be  seen.  Between  these  positions 
any  part  may  be  visible.  The  base  of  the  cone  being  at 
right  angles  to  its  axis,  as  in  the  cylinder,  it  must  appear 
as  an  ellipse  whose  long  axis  is  perpendicular  to  the  axis  of 
the  cone.  In  Fig.  56  more  than  half  the  curved  surface  of 
the  cone  is  visible ;  in  Fig.  57  less  than  half ;  and  in  Fig. 
58  nearly  all  is  seen. 

To  draw  the  cylinder,  cone,  or  similar  object,  the  method 
illustrated  by  the  box  should  be  followed,  the  mass  being 
blocked  in  first.  In  the  case  of  all  symmetrical  objects 
having  an  axis,  this  imaginary  line  should  not  be  drawn 
first  as  is  often  recommended,  but  after  the  proportion  and 
position  has  been  secured,  the  drawing  may  be  tested  by  a 
centre  line  before  lining  it  in.  On  no  account  should  this 
line  be  drawn  first. 


38  PERSPECTIVE   PRINCIPLES. 


COKCENTRIC    CIRCLES. 


Eig.  59.  Concentric  circles  must  appear  ellipses  whose 
directions  are  the  same,  but  since  the  centre  of  the  circle 
doeg  not  appear  the  centre  of  the  ellipse,  the  long  axis  of 
the  larger  ellipse,  line  A-B,  comes  in  front  of  the  long  axis, 
G-H,  of  the  smaller  ellipse.  The  smaller  circle  is  half  the 
diameter  of  the  larger,  and  a  diameter,  C-D,  of  the  larger 
circle  is  divided  into  four  equal  parts  by  the  inner  circle. 
Although  the  diameters  of  the  ellipses  do  not  coincide,  they 
are  generally  so  little  apart  that  the  equal  divisions  of  the 
diameter  of  the  circle  are  nearly  enough  represented  by 
equal  spaces  on  the  long  axis  of  the  larger  ellipse.  The 
equal  distances  on  the  diameter,  E-F,  appear  perspectively 
equal  (Fig.  13),  so  that  practically  we  may  say  that  if  the 
distance,  H-B,  is  one-fourth  of  the  axis,  A-B,  the  short 
axis,  E-E,  will  have  the  distances  E  1  and  F  3  perspective 
fourths  of  the  entire  length,  E-F.  Thus,  in  Fig.  60  the 
distance,  0-1,  is  one-sixth  of  the  long  axis,  0-6,  and  the  dis- 
tance, a-b,  is  perspectively  one-sixth  of  the  short  axis,  a-g. 
This  will  enable  us  to  test  the  drawing  of  the  ring  (Fig.  61), 
in  which  we  must  further  see  that  the  thickness  (which  is 
given  by  the  lines  1-2,  3-4  and  5-6,  all  being  equal  in  the 
object)  shall  in  the  drawing  be  so  perspectively,  the  nearest 
1-2  being  the  longest,  and  the  farthest  5-6  being  the  short- 
est. This  figure  illustrates  the  fact  that  in  most  drawings 
from  nature  there  will  be  but  a  very  little  distance  between 
the  axes  of  the  ellipses  representing  concentric  circles.  In 
this  drawing  we  see  that  the  retreating  parallel  circles  do 


PERSPECTIVE    PRINCIPLES.  39 

not  appear  to  come  together  as  they  recede  until  the  further 
half  of  the  circle  is  reached.  Thus  we  see  that  curved, 
parallel  retreating  lines  may  appear  to  converge  or  diverge. 

FRUSTUM   OF  PYRAMID   AND  CONE. 

When  any  pyramid  is  cut  by  a  plane  parallel  to  its  base, 
the  section  is  similar,  and  its  edges  are  parallel  to  those  of 
the  base.  "When  drawing  this  form  this  fact  must  be  kept 
in  mind ;  and  also  that  the  slant  edges  continued  must 
meet  in  the  axis  of  the  solid.  The  legs  of  stools,  chairs 
and  tables  present  this  form.  The  draAvings  of  such  ob- 
jects should  be  tested  by  continuing  the  legs  to  see  that 
they  meet  at  a  point  over  the  centre  of  the  base  (Fig.  62). 

The  frustum  of  the  cone  (Fig.  63)  is  a  form  found  in 
many  common  objects.  Frequently  there  are  rings  about 
the  cone  (Fig.  64).  As  already  shown,  the  visible  curved 
surface  of  the  cone  may  range  from  the  entire  surface  to 
none.  When  there  are  circles  or  rings  about  its  surface, 
they  will  show  in  the  same  proportion  as  the  surface  con- 
taining them.  Thus,  when  the  cone  inclines  toward  the 
eye,  more  than  half  the  ellipses  representing  the  rings  will 
be  seen,  and  Avhen  the  cone  inclines  from  the  eye  a  small 
part  will  be  visible  (Fig.  ^i)).  In  this  figure  it  will  be 
noticed  that,  if  the  middle  ellipse  at  the  front  comes  mid- 
way between  the  top  and  the  bottom,  behind  its  posi- 
tion will  be  the  same  (perspectively).  This,  and  the  fact 
that  the  width  of  the  ellipse  must  increase  proportionally 
until  the  further  circle  is  reached,  will  enable  such  lines  to 
be  drawn  correctly. 


40  PERSPECTIVE  PRIXCIPLES. 

In  Fig.  66  the  width,  of  the  band  A  seems  greatest  at  the 
sides  because  there  it  is  foreshortened  less  than  in  front. 
The  width  of  the  bands,  A-A,  will  be  greater  or  less  at  the 
sides  according  to  the  angle  of  the  cone,  and  the  direction 
in  which  it  is  seen.  When  the  cone  has  its  larger  base 
visible  (Fig.  65),  the  nearer  part  of  the  band  will  appear 
widest  at  its  nearest  point. 

The  drawing  of  the  dish  (Fig.  67)  shows  that  the  nearest 
part,  since  it  inclines  away,  may  appear  narrower  than 
the  side  of  the  dish  at  the  back.  However,  it  is  impos- 
sible to  state  a  rule  for  all  the  above  shapes  regarding 
appearance. 

In  the  double  cone  (Fig.  68)  the  smaller  circle  A  is  com- 
mon to  both  surfaces.  Since  one  of  the  cones  must  incline 
away  from  the  eye,  less  than  half  of  the  ellipse  can  be 
visible.  The  contour  elements  of  each  cone  must  be  tan- 
gent to  the  ellipse,  and  those  of  the  farther  cone  will  inter- 
sect or  pass  behind  those  of  the  nearer  cone. 

The  torus  is  a  plinth  with  a  circular  top  and  bottom, 
connected  by  a  surface  whose  section  is  a  semicircle.  This 
form  is  very  common  in  furniture.  It  may  be  represented 
correctly  by  drawing  first  the  plinth  of  which  the  plane 
surfaces  are  the  ends.  If  a  semicircle  be  drawn  from  the 
ends  of  the  long  axes  of  the  two  ellipses,  and  a  line  be 
drawn  tangent  to  the  semicircle  and  to  the  ellipses  above 
and  below,  this  line  will  be  the  outline  of  the  torus  (Fig.  69). 
When  the  ellipses  are  wide,  and  the  drawing  large,  the 
outline  will  come  a  little  outside  that  of  the  plinth  at  front 
and  back. 


PERSPECTIVE  PRINCIPLES.  41 

THE   RING   OF  CIRCULAR   SECTION. 

(Fig.  70).  This  object  will  be  represented  by  two  concen- 
tric circles  when  it  is  directly  in  front,  but  when  fore- 
shortened its  outlines  will  not  be  ellipses.  This  is  due  to 
the  fact  that  the  rays  come  tangent  below  in  front ;  and 
behind,  above  the  centre  of  the  ring,  and  the  line  on  the 
rin^  which  is  on  the  contour  is  not  a  circle.  When  much 
foreshortened  the  further  inner  outline  will  pass  behind  and 
intersect  the  line  which  represents  the  nearer  part.  This 
drawing  may  be  tested  by  the  centre  line  of  the  object, 
which  is  a  circle  and  appears  an  ellipse.  Draw  this  ellipse, 
and  suppose  a  sphere  to  pass  around  the  circle.  The  centre 
of  the  sphere  being  in  the  circle,  its  surface  must  describe 
the  surface  of  the  ring.  The  sphere  will  be  represented  by 
circles  whose  centres  are  in  the  ellipse,  the  one  behind 
being  slightly  smaller  than  the  nearer.  The  ring  must  be 
represented  by  lines  drawn  tangent  to  these  circles. 

FRAMES. 

Any  objects  of  the  geometric  forms,  constructed  of  pieces 
of  uniform  size,  may  be  tested  by  means  of  the  diagonals  of 
the  figure,  for  polygons  whose  sides  are  parallel  and  whose 
centres  coincide  have  the  same  diagonals.  Thus,  in  the 
frame,  Fig.  71,  if  the  line  A  be  drawn,  its  intersection  with 
the  diagonals  must  give  the  extremities  of  lines  B  and  C. 
In  the  cubical  frame,  by  continuing  the  line  A  to  the  edge 
1-2,  a  point  in  the  line  E  is  secured. 

In  the  triangular   frame  the   perpendicular   from   each 


42  PERSPECTIVE  PRINCIPLES. 

angle  to  the  opposite  side  gives  the  angles  of  the  inner 
figure,  and  any  side,  as  A,  being  drawn,  the  lines  B  and  C 
will  extend  from  1  and  2,  parallel  perspectively  to  the  sides 
of  the  outer  figure. 

In  hexagonal  and  other  frames  the  same  principle  will 
apply. 

Fig.  74  presents  forms  frequent  in  furniture.  The  upper 
form  A  consists  of  a  ring  outside  a  cylinder,  and  is  really 
the  form  found  in  the  torus,  explained  on  page  40.  The 
lower  form  C  is  a  v-shaped  groove  cut  into  the  cylinder. 
This  is  the  double  cone  explained  on  page  40.  The  inner 
form  B  is  a  semicircular  groove.  This  will  be  represented 
by  two  ellipses,  showing  the  circular  edges,  and  when  the 
ellipses  are  wide  and  the  groove  is  narrow  nothing  but  the 
ellipses  can  be  seen,  as  at  D.  If  the  ellipses  are  narrow, ' 
and  the  groove  is  wide,  the  curved  surface  will  be  repre- 
sented by  a  curved  line  (as  shown  in  the  figure),  which  ends 
above  the  diameter  of  the  ellipse.  A  similar  line  is  found 
in  vase  forms  when  the  stem  joins  the  base  (Fig.  75). 

VASE    FORMS. 

In  Fig.  76  we  have  in  elevation  a  common  form,  in  which 
there  are  three  circles  represented  by  straight  lines.  Fig. 
77  is  a  model  drawing  of  the  same  form  in  which  the  circles 
are  represented  by  ellipses.  A  common  mistake  is  shown 
at  the  right  side,  where  the  outline  of  the  body  is  drawn  to 
the  end  of  the  long  axis  of  the  ellipse.  The  line  is  cor- 
rectly placed  at  the  left.  It  must  come  tangent  to  the 
ellipse  at  the  back,  and  thus  pass  above  the  end  of  the  long 


PERSPECTIVE    PRINCIPLES.  43 

axis.  Another  point  wliich  is  frequently  iinnoticed  is,  that 
when  the  handle  of  a  vase  seems  to  extend  from  its  outline, 
it  intersects  the  vase  in  a  line  inside  the  outline  (Fig.  78), 
and  the  more  the  handle  extends  toward  the  eye  the  fuller 
the  line  of  its  intersection  with  the  vase. 

Fiir.  79  is  a  side  view  of  a  vase.  The  exact  dimensions 
of  the  model  drawing  (Fig.  80)  may  be  obtained  by  sup- 
posing the  eye  at  a  certain  distance,  and  drawing  the  visual 
rays  to  intersect  the  picture  plane,  which  is  placed  at  right 
angles  to  them  (see  side  elevation).  The  top  of  the  vase 
being  against  the  picture  plane,  the  long  axis  of  the  top 
ellipse  will  be  very  nearly  the  full  diameter  of  the  top. 
The  circles  below  being  behind  the  picture  plane,  a  little 
must  be  allowed  for  the  effect  of  perspective,  as  well  as  for 
the  fact  that  the  long  axis  of  the  ellipse  is  not  a  diameter 
of  the  circle.  In  this  vase  there  are  three  plinths,  A,  B 
and  C,  whose  circles  will  appear  ellipses.  The  curve  of  the 
neck  will  intersect  the  under  ellipse  of  the  top,  and  will 
end  below  as  in  Fig.  75.  The  curve  of  the  body  of  the 
vase  must  come  tangent  behind  to  the  lower  ellipse  of  the 
middle  band,  as  explained  in  Fig.  77. 

Fig.  81  shows  the  lower  part  of  a  vase.  It  consists  of 
the  spherical  body  and  a  cylinder  with  a  round  edge  as 
base.  The  round  edge  is  a  thin  torus,  and  should  be  drawn 
as  illustrated  by  Fig.  74.  The  cylinder  intersects  the  body 
in  a  circle,  which  appears  an  ellipse.  If  the  ellipse  is  nar- 
row, part  of  it  will  be  visible,  but  the  outline  of  the  body 
must  come  tangent  to  it,  and  cover  the  ends  of  the  axis  of 
the  ellipse  (Fig.  82).     If  the  ellipse  is  wide  the  curve  may 


44  PERSPECTIVE  PRINCIPLES. 

come  tangent  in  front,  as  in  Fig.  83,  and  if  the  ellipse  is 
wider  it  will  be  invisible  behind  the  outline  of  the  body 
(Tig.  84). 

Fig.  85  gives  a  side  view  of  the  top  and  bottom  of  another 
vase.  The  top  consists  of  two  cone  forms,  with  a  cylindri- 
cal band  between  them.  There  are  five  circles,  and  to  re- 
present the  top,  four  ellipses  and  the  ends  of  the  fifth  must 
be  drawn.  The  body  and  the  base  are  connected  by  a  cylin- 
der. The  body  will  be  represented  by  lines  tangent  to  the 
upper  ellipse  at  the  front,  as  in  Fig.  82.  The  curve  of  the 
base  will  be  tangent  to  the  lower  ellipse  behind,  as  in  Fig. 
77.  The  lower  edge  is  the  frustum  of  a  cone,  and  in  this 
form  the  straight  lines  tangent  to  the  ellipses  must  not  be 
forgotten,  as  is  apt  to  be  the  case,  especially  when  the 
ellipses  representing  the  two  bases  intersect,  as  at  the  top 
when  the  straight  line  can  hardly  be  seen,  and  when  knowl- 
edge only  will  produce  an  exact  drawing. 

The  principles  which  have  been  explained  will  enable  one 
to  see  as  it  is  impossible  to  see  without  them,  and  to  draw 
without  the  objects,  to  draw  from  memory,  and  to  design 
geometric  forms  of  any  size  and  in  any  position.  They  will 
be  of  so  much  use  to  the  practical  draughtsman  that  he  can- 
not afford  to  be  without  them,  even  were  it  very  difficult  to 
obtain  this  knowledge.  The  principles  are,  however,  so 
simple  that  there  is  no  excuse  for  violations  of  the  few 
essential  ones;  but  such  violations  are  found  very  frequently 
not  only  in  the  work  of  the  amateur,  but  also  in  that  of  the 
professional  draughtsman. 

The  student  who  has  a  knowledge  of  working  drawings 


PERSPECTIVE    PRIKCIPLES.  45 

may  test  his  ability  to  draw  from  a  description  of  the  form 
and  its  position,  by  taking  any  sheets  of  projection  show- 
ing objects  one  after  another,  supposing  them  to  be  seen 
from  a  certain  point,  and  making  model  drawings  which 
shall  represent  them.  Thus,  Fig.  87  is  a  working  drawing 
showing  several  objects,  and  their  relations  to  each  other, 
and  the  planes  of  the  drawing,  and  Fig.  88  is  a  model 
drawing  of  the  same. 

We  will  suppose  the  objects  to  be  seen  from  the  left  and 
from  above  so  that  three  faces  of  the  cube  are  visible. 

The  cube  is  the  first  object,  and  any  drawing  which  shows 
the  top,  front  and  left  sides  answers  the  requirement.  When 
the  cube  is  correct  the  G.  L.  which  is  parallel  to  the  edges 
extending  to  the  right  should  be  drawn. 

The  cone  is  the  next  object.  Its  base  is  a  circle  of  the 
same  diameter  as  the  base  of  the  cube.  The  best  way  to 
place  the  ellipse  which  is  the  appearance  of  this  circle  is  to 
draw  a  square  whose  sides  are  parallel  to  the  base  of  the 
cube.  The  ellipse  must  come  tangent  to  the  square  at  its 
diameters.  The  distance  between  the  cone  and  the  cube  is 
equal  to  half  the  side  of  the  cube.  This  distance  1-2,  will 
be  found  by  drawing  the  diagonals  of  the  right  front  face 
of  the  cube,  and  set  off  on  line  A-B  from  2  to  3  gives  the 
nearest  angle  of  the  square.  Its  sides  extending  to  the 
right  are  continuations  of  and  are  perspectively  equal  to 
those  of  the  first  square ;  and  the  sides  extending  to  the 
left  are  parallel  to  those  of  the  first.  It  should  be  remem- 
bered that  these  lines  continue  and  vanish  at  right  and  left 
in  a  horizontal  at  the  level  of  the  eye,  and  all  parallel  lines 


46  PERSPECTIVE  PRINCIPLES. 

should  be  continued  as  far  as  the  drawing  will  allow,  so  that 
they  may  be  given  the  proper   convergence.      The  student 
should  not  attempt  to  have  the   vanishing  points  come  on 
the  paper.    The  diameters  of  the  base  being  drawn,  give  the 
tangent  points  of  the  circle  and  square,  and  through  them 
the  ellipse  must  pass.      The  circle   is  horizontal,  and  the 
axis  of  the  ellipse  must  be  a  horizontal  line.     The  distance 
between  the  centre  of   the  ellipse  and  the  centre  of    the 
square  is  so  slight  as  to  be  hardly   noticeable.      The  long 
axis  of  the  ellipse  must  be,  however,  in  front  of  the  centre 
of  the  square ;  and  in  a  larger  drawing  where  the  ellipse  is 
wide,  if  the  axis  should  be  drawn  through  the  centre,  the 
error  would  be  very  noticeable.    The  axis  passes  through  the 
centre  of  the  square,  and  must  be  represented  by  a  vertical 
line.     Its  length  is  readily  determined  by  reference  to  the 
vertical  edges  of  the  cube,  which  are  half    as  long  as  the 
axis. 

The  cylinder  is  next  to  be  considered.  The  front  circle 
is  in  the  plane  of  the  front  face  of  the  cube,  and  it  will  be 
best  drawn  by  means  of  the  square  which  circumscribes  it. 
The  sides  of  the  square  are  parallel  and  equal  to  those  of 
the  front  right  face  of  the  cube.  Of  course  the  distance 
5-6  must  be  less  than  3-4,  as  3-4  is  less  than  1-2,  and  4-5  is 
less  than  2-3  (See  Fig.  13).  The  diagonals  of  the  square 
give  its  centre,  and  through  this  point  the  axis  of  the  cyl 
inder  must  pass.  The  vertical  and  horizontal  diameters 
give  four  points  in  the  ellipse,  whose  long  axis  is  a  little  in 
front  of  the  centre  of  the  square,  and  at  right  angles  to  the 
axis  of  the  cylinder.    In  the  same  way  the  further  end  may 


PERSPECTIVE  PRINCIPLES.  47 

be  drawn.     The  length  of  the  cylinder  being  twice  the  side 
of  the  cube,  the  distance  7-8  is  perspectively  equal  to  5-7. 

The  hexagonal  prism  is  the  last  object.  It  is  vertical 
with  one  face  in  the  plane  of  the  line  A-B.  A  diagonal  of 
its  base  is  parallel  to  A-B.  Its  length  may  be  placed  on 
A-B  from  9  to  10,  perspectively  equal  to  5-6,  the  distance  6-9 
being  perspectively  equal  to  4-5.  Points  11,  12  and  13 
dividing  9-10  into  four  perspectively  equal  parts,  being 
placed,  the  diameters  of  the  hexagon  will  extend  from 
4  and  13  to  the  left  vanishing  point.  The  side  14-15  having 
been  drawn,  the  diagonals  11-15  and  13-14  give  the  centre. 
Through  this  point  the  diagonal  parallel  to  11-13  passes, 
and  the  lines  from  9-10  give  in  it  the  two  remaining  angles 
of  the  base  16  and  17.  The  left  vertical  face  is  the  narrower. 
This  shows  that  16  is  nearer  than  13  and  the  diameter  16- 
13  inclines  upward  slightly  from  16. 

These  drawings  will  call  for  lines  at  definite  angles  with 
the  ground  and  the  vertical  plane.  Such  angles  may  be 
determined  by  means  of  the  cube,  and  for  this  reason  it  will 
be  well  to  draw  this  object  first,  even  when  it  is  not  called  for 
(Fig.  89).  The  edges  of  the  cube  being  perpendicular  to 
the  two  planes,  the  diagonals  of  its  faces  are  at  forty-five 
degrees.  If  smaller  angles  are  desired  they  can  be  obtained 
by  subdividing  the  angles  of  forty-five  degrees.  In  making 
this  division  it  must  be  noticed  that  equal  angles  never  aj)- 
pear  equal  when  occupying  different  positions  with  regard  to 
the  picture  plane.  Pig.  90  shows  that  equal  angles  appear  un- 
equal and  larger  the  more  the  lines  of  the  angles  are  foreshort- 
ened, so  that  to  divide  any  angle,  tna  part  whicn  is  most  nearly 


48  PERSPECTIVE    PRINCIPLES. 

directed  toward  the  eye,  must  be  represented  by  the  greater 
angle,  and  as  equal  angles  approach  the  position  of  directly 
in  front  they  will  appear  smaller.  Such  practice  will  more 
quickly  than  anything  else  sIioav  the  student  whether  he 
really  understands  the  principles,  or  has  been  merely  memo- 
rizing them.  The  latter,  which  unfortunately  is  the  only 
way  many  students  study,  will  be  found  entirely  useless, 
and  those  who  have  been  working  thus,  must  start  again 
with  the  determination  to  see  with  their  own  eyes,  and 
accept  nothing  which  they  have  not  verified  by  careful 
study. 


INTERIORS  AND  GENERAL  WORK. 

All  drawings,  whatever  the  subject,  should  be  carried  on 
in  the  same  way,  first  by  blocking  in  the  mass  of  the  whole, 
and  then  the  masses  of  the  various  parts,  the  detail  coming 
last.  In  drawing  from  objects  having  curved  lines,  the 
student  should  be  careful  not  to  be  content  with  the  general 
effect  of  the  line,  but  should  in  finishing  see  that  he  does 
not  lose  the  character,  which  is  given  by  the  slight  changes 
in  direction  which  occur  in  many  lines.  Thus,  in  drawings 
from  the  cast,  lines  which  at  first  glance  seem  of  uniform 
curvature,  will  be  found  to  be  composed  of  many  short 
lines,  having  different  directions,  and  often  straight  or 
nearly  so.  The  student  will  get  the  character  only  by  look- 
ing for  these  short,  straight  lines  ;  but  this  method  of  draw- 
ing curves  must  not  lead  him  to  put  straight  lines  where 
none  can  be  seen,  as,  for  instance,  in  an  ellipse. 

After  the  groups  of  geometric  solids,  common  objects, 
boxes,  furniture,  etc.,  should  be  taken.  These  may  be  ar- 
ranged in  groups ;  and  here  the  student  may  study  to  make 
a  pleasing  arrangement.  This  work  leads  directly  to  the 
drawing  of  interiors.  Xo  principles  other  than  those  ex- 
plained with  the  geometric  solids  are  involved.  The  only 
question  or  difficulty  likely  to  arise  will  come  from  the 
larger  space  to  be  represented.  As  this  space  is  not  defi- 
nitely outlined,  the  whole  cannot  be  blocked  in  as  in  a 
group  of  models.  The  best  way  will  be  to  draw  the  central 
group  or  the  most  prominent  mass  of  the  subject  first,  and 

(49) 


60  INTERIORS    AND    GENERAL    "WORK. 

then  add  the  surrounding  parts.  It  -will  be  well  to  take  for 
comparison  some  long  and  important  line  of  the  central 
mass.  If  care  is  exercised  in  determining  the  proportions 
of  the  rest,  with  this  line  as  unit,  the  smaller  subdivisions 
of  each  space  will  come  without  trouble. 

In  this  work,  as  in  all,  the  aim  should  be  to  represent 
as  nearly  as  possible  the  appearance  of  everything.  The 
subject  being  larger,  and  the  straight  lines  longer,  their 
apparent  curvature  is  often  sufficient  to  be  most  noticeable, 
and  as  we  do  not  wish  to  represent  straight  lines  by  curved, 
it  is  evident  that  we  cannot  draw  everything  just  as  we  see 
it.  See  pages  24  and  71.  It  will  be  well  to  avoid  the  repre- 
sentation of  a  wall  which  extends  far  on  both  sides  of  the 
spectator,  as  this  will  make  the  drawing  very  different  from 
the  appearance.  If  one  wall  only  is  to  be  represented  it  is 
better  to  draw  from  one  end  of  the  room,  and  thus  cause  the 
lines  to  vanish.  When  two  walls  are  shown  they  will  both 
vanish.  When  three  are  to  be  represented  the  middle  one 
must  have  no  vanishing.  Fig.  91  shows  that  were  it  to 
vanish  the  whole  of  the  left  wall  (and  of  course  the  further 
edge.  A,  must  appear  shorter  than  the  nearer,  B)  would  be 
outside  of  both  vanishing  points  of  the  drawing,  and  the 
distortion  of  all  to  the  left  of  the  left  vanishing  point  would 
be  most  marked.  In  general,  when  any  horizontal  lines 
extend  on  both  sides  of  the  spectator,  they  should  be  repre- 
sented by  horizontal  lines. 

In  interiors  it  is  sometimes  necessary  to  draw  as  the  room 
would  appear  from  a  supposed  position  far  enough  away  to 
show  more  than  can  be  seen  from  any  attainable  position. 


INTERIORS    AND'  GENERAL    WORK.  51 

Such  drawings  will  call  for  a  thorough  knowledge  of  all  the 
principles. 

In  interiors  and  in  street  scenes  there  is  not  only  the 
question  of  horizontal  foreshortening  to  be  considered,  but 
also  vertical.  It  is  impossible  to  make  a  sketch  which  shall 
include  an  extended  range  of  vision,  and  shall  give  the 
exact  appearance  of  each  part  and  also  of  the  whole.  We 
get.^the  real  dimensions  of  the  appearance  of  any  object  on 
a  plane  which  is  perpendicular  to  the  rays  to  the  object. 
Carry  this  principle  out,  and  the  surface  which  gives  the 
exact  appearance  of  an  extended  range  is  that  of  a  sphere 
which  cannot  be  developed.  This  then  is  the  reason  why 
we  cannot  always  draw  just  what  we  see. 

The  space  which  can  be  included  in  a  model  drawing,  and 
which  may  be  represented  ou  a  plane  without  noticeable 
distortion,  should  not  include  an  angle  at  the  eye  of  over 
twenty-eight  degrees.  If  this  is  much  exceeded,  the  ques- 
tions of  the  curvature  of  parallel  lines  both  for  horizontal 
and  vertical  distances  will  arise,  but  as  most  drawings  re- 
quire a  larger  angle  the  question  must  be  considered. 

The  mind,  knowing  lines  to  be  straight,  will  hesitate  to 
accept  their  representation  by  curved  lines,  or  knowing 
them  to  be  vertical,  will  not  accept  readily  their  representa- 
tion by  inclined  lines.  The  draAving  should  give  the  im- 
pression of  nature  as  far  as  possible,  even  when  the  eye  is 
not  at  the  proper  distance.  The  impression  of  vertical 
lines  is  given  by  vertical  lines,  and  of  straight  lines  by 
straight  lines.  For  this  reason  it  seems  best  that  the  stu- 
dent should  represent  what  he  sees  as  nearly  as  possible, 


52  INTERIORS    AND    GENERAL    WORK. 

but  in  accordance  with  the  perspective  principle  that  straight 
lines  shall  be  represented  by  straight  lines.  This  will  cause 
him  to  represent  straight  edges,  which  extend  on  both  sides 
by  parallel  horizontal  lines,  and  to  substitute  for  the  curved 
lines  found  in  buildings,  at  angles  with  the  picture,  straight 
lines  extending  to  two  vanishing  points.  This  will  change 
the  drawing  very  little,  as  shown  on  page  72. 

In  drawings  of  street  scenes  the  lines  are  long  and  broken, 
and  the  curvature  may  not  be  noticed  if  each  part  is  drawn 
as  it  appears.  In  these  subjects  also,  one  does  not  know 
what  the  conditions  are  (the  edges  might  be  curved  in 
nature),  and  so  there  is  not  the  contradiction  between  the 
knowledge  of  the  facts  and  their  appearances.  If  the  artisc 
chooses  to  represent  straight  by  curved  lines  he  has  nature 
as  authority,  and  the  example  of  noted  predecessors,  and 
no  one  would  wish  to  say  that  his  drawing  was  not  good, 
or  that  it  would  be  improved  by  plane  perspective.  Whether 
or  no,  the  foreshortening  of  horizontal  and  vertical  distances 
shall  always  be  given,  is  a  question  which  can  be  answered 
only  as  it  arises,  and  decided  according  to  the  conditions  of 
the  subject  and  the  aim  of  the  drawing.  It  is  a  question 
for  the  artist  rather  than  the  student,  who  should,  until  he 
has  attained  by  long  practice  ability  to  judge  proportions 
correctly,  never  be  permitted  to  draw  other  than  those 
he  sees. 


TESTS. 

In  beginning,  the  student  should  understand  that  the 
drawings  are  of  no  value  in  themselves,  but  are  of  use  only 
as  they  train  the  eye  to  see  correctly.  The  eye  can  be 
taught,  or  rather  the  mind  can  be  made  to  accept  the  image 
of  the  eye  only  by  depending  upon  it,  and  if  the  student 
begins  by  measuring  and  testing  he  will  never  be  able  to 
draw  otherwise.  This  is  undesirable  for  many  reasons,  the 
most  important  being  that  no  measurements  or  tests  can  be 
applied  which  will  take  the  place  of  correct  perception,  or 
begin  to  equal  it  in  exactness.  It  is  thus  most  important 
that  the  student  from  the  beginning  depend  entirely  for  his 
first  drawing  upon  his  perception  of  its  appearance. 

The  readiest  way  of  determining  the  proportions  of  an 
object  is  by  the  use  of  a  pencil,  or  other  straight,  slender 
rod,  held  at  arm's  length,  and  made  to  cover  the  lines  to  be 
compared.  Thus  the  top  of  the  pencil  may  be  made  to 
cover  the  top  of  the  object,  and  the  thumb-nail  held  against 
the  pencil  to  cover  the  bottom  of  the  object.  If  the  pencil 
is  then  turned  into  a  horizontal  position,  the  height  of  the 
group  may  be  compared  with  its  width.  If  the  measure- 
ment covering  the  height  extends  over  one-half  the  width, 
the  object  appears  twice  as  wide  as  high.  In  this  way  the 
proportions  of  any  object  or  group  may  be  determined.  It 
is  important  that  the  student  should  see  that  such  use  of 
the  pencil  is  simply  to  obtain  the  proportion  of  height  to 
width,  and  not  to  determine  the  actual  size  of  the  drawing. 

(53) 


54  TESTS. 

In  fact  this  use  of  the  pencil  should  not  be  allowed,  for  the 
eye  and  hand  will  be  in  different  positions  when  taking  the 
various  measurements,  and  if  they  are  transferred  to  the 
paper,  as  is  the  wish  of  many  beginners,  the  drawings  re- 
sulting will  be  entirely  out  of  proportion.  The  slightest 
change  in  the  distance  of  the  pencil  from  the  eye  in  com- 
paring proportions  will  occasion  great  inaccuracy.  The 
only  way  to  be  at  all  correct  is  to  hold  the  pencil  as  far 
from  the  eye  as  possible,  the  arm  being  perfectly  straight, 
and  the  pencil  being  turned  by  twisting  the  entire  arm. 
The  pencil  must  be  at  right  angles  to  the  direction  in  which 
we  look  for  the  measurement.  Xearly  all  students  have 
the  idea  that  this  means  parallel  to  the  side  of  the  room  or 
the  bench  upon  which  the  object  is  resting.  This,  however, 
is  wholly  false,  for  the  position  of  the  object  with  reference 
to  its  surroundings  is  of  no  consequence,  and  must  not  be 
considered.  If  the  student  has  a  cube  to  represent  he  must 
look  at  it,  and  the  plane  which  gives  its  real  appearance 
must  be  perpendicular  to  the  direction  in  which  he  looks, 
and  the  pencil  must  always  be  held  thus  when  taking  meas- 
urements. A  good  way  is  to  find  some  position  in  the 
fingers  in  which  the  pencil  will  be  perpendicular  to  the 
arm,  and  the  arm  being  outstretched  will  bring  the  pencil 
into  practically  the  correct  position  (Fig.  92).  Those  who 
cannot  do  this  readily,  and  who  do  not  hold  the  pencil 
rightly,  will  find  that  a  pin  stuck  into  the  pencil  at  right 
angles  to  it,  in  such  a  position  that  it  may  be  seen  while 
taking  the  measurements,  will  correctly  place  the  pencil. 
When  the  pencil  is  held  so  that  only  the  head  of  the  pin 


TESTS.  55 

can  be  seen,  it  must  be  perpendicular  to  the  direction  in 
which  the  student  looks  (Fig.  93).  But  a  much  better 
device  may  be  made  by  bending  a  piece  of  soft  wire  (a  hair- 
pin), about  a  large  knitting  needle,  as  shown  in  Fig.  94, 
so  that  one  end  will  project  at  right  angles  to  the  needle, 
and  the  other,  after  passing  around  the  needle  several  times, 
shall  extend  back,  and  project  a  little  distance  perpendicu- 
lar to  the  first  end.  The  long  end,  at  right  angles  to  the 
needle,  will  place  the  needle  correctly.  The  wire  should 
press  the  needle  just  enough  to  keep  it  in  position.  It  may 
be  moved  by  the  finger  or  thumb,  and  the  measurement 
taken  by  sighting  by  the  short  end.  This  slide  will  be 
found  of  very  great  assistance,  and  as  it  is  important  that 
measurements  should  be  exact,  it  is  desired  that  every  stu- 
dent be  provided  with  this  measuring  rod.  It  will  also  be 
found  a  great  help  when,  as  is  generally  the  case,  one  meas- 
urement is  not  an  easily  determined  part  of  the  other.  In 
measuring,  the  smaller  measurement  should  be  taken  first, 
and  then  compared  with  the  larger.  If  the  former  is  one- 
half  or  one-third  of  the  latter  it  will  be  easily  determined ; 
but  if  the  first  goes  once  and  a  fractional  part,  as  one-fifth 
or  one-sixth,  this  part  is  not  easy  to  determine,  and  if  the 
two  measurements  can  be  secured  in  such  a  way  that  they 
may  be  compared  at  length,  the  proportions  may  be  more 
surely  determined.  This  may  be  done  by  taking  the  smaller 
measurement  by  the  sliding  wire,  and  the  larger  by  the 
thumb,  and  in  this  way  the  two  can  be  compared  at  leisure. 
Much  care  must  be  taken  that  the  distance  of  the  reedle 
from  the  eye  shall  be  the  same  for  all  lines  compared  with 


56  TESTS. 

each  other.  The  distance  is  so  apt  to  vary  that  unless  each 
comparison  be  made  several  times  -with  the  same  result, 
there  is  little  chance  of  the  measurement  being  correct.  It 
is  useless  to  think  that  tests  not  carefully  taken  are  worth 
the  time  given  them,  and  it  is  much  better  to  take  the  one 
proportion  of  height  and  width  carefully  than  to  spend  the 
time  necessary  to  do  this  on  half  a  dozen  measurements, 
which  are  sure  to  contradict  and  do  more  harm  than 
good. 

It  is  impossible  to  compare  accurately  a  short  distance 
with  a  long.  If  the  height  is  equal  to  or  one-half  the  width, 
care  will  so  determine  it,  but  with  every  change  of  the  hand 
in  moving  a  short  distance  over  a  long  inaccuracy  is  pro- 
duced, so  it  is  well  to  avoid  all  such  comparisons.  The 
inaccuracy  arises  from  inability  to  hold  the  pencil  at  exactly 
the  right  place,  also  from  the  change  in  distance  of  the  pen- 
cil, which  every  movement  away  from  the  first  position  occa- 
sions. This  movement  may  be  seen  to  occur  by  tying  a  thread 
to  the  pencil,  and  measuring  the  distance  of  the  pencil  from 
the  eye,  by  holding  the  thread  with  a  finger  of  the  left  hand 
against  the  brow.  If  the  arm  is  dropped  for  the  measure- 
ment of  a  near  object,  and  the  string  is  tight,  it  will  slacken 
when  the  arm  is  raised,  and  in  the  same  way  it  will  change 
for  horizontal  movement.  The  only  way  then  in  which 
really  exact  measurements  can  be  taken,  will  be  by  the  use 
of  such  a  measuring  thread  for  the  pencil,  but  we  wish  to 
simplify  the  subject  as  much  as  possible,  and  if  reasonable 
care  is  exercised  the  variation  of  the  distance  of  the  needle 
may  be  made  so  slight  as  to  be  unimportant,  at  least  in  the 


TESTS.  57 

first  part  of  our  work,  wliich  will  consist  iu  the  drawing  of 
small  objects,  singly  or  in  groups. 

Whenever  possible  all  comparisons  should  be  made  by 
swinging  the  pencil  from  a  vertical  into  a  horizontal  posi- 
tion by  a  motion  of  the  whole  arm  from  the  shoulder,  and 
avoiding  a  change  of  position  of  the  pencil,  by  sicinging  it 
about  one  end  of  the  first  measurement.  Thus,  if  the  height 
and  width  of  a  table  is  desired,  instead  of  measuring  the 
width  along  the  top,  and  then  dropping  the  hand  to  take 
the  vertical  measurement  (which  will  be  done  by  almost  all 
students,  or  what  amounts  to  this,  the  measurement  of  the 
height  and  the  lifting  of  the  hand  for  comparison  with 
width),  make  the  measurement  by  taking  the  width  along 
the  top,  and  swing  the  pencil  down  about  the  thumb,  thus 
not  changing  the  distance  of  the  hand.  The  easier  way 
will  be  to  take  the  measurement  at  the  bottom,  and  swing 
the  pencil  up  about  the  thumb  (see  Fig.  95).  This  way  of 
measuring  will  be  easily  acquired,  and  will  assist  very 
greatly  to  correctness. 

A  short  distance  may  of  course  be  compared  with  a  long 
with  a  degree  of  accuracy  which  varies  with  the  student, 
but  such  measurements  are  not  recommended,  and  are  not 
necessary,  as  other  tests  will  bring  better  results.  Another 
way  by  which  distances  may  be  compared  is  by  marking 
upon  the  edge  of  a  straight-edge  or  bit  of  cardboard  with  a 
pencil,  and  then  comparing  at  leisure.  The  use  of  the  pin 
or  the  needle  with  a  sliding  wire  may  be  necessary  at  first 
for  most  students,  but  after  practise  these  helps  will  not  be 
required,  and  the  pencil  will  be  held  correctly  without  diffi- 


58  TESTS. 

culty.  If  the  back  end  of  the  pencil  is  used  to  measure  by, 
the  pencil  will  be  placed  correctly  when  the  end  is  seen  as 
a  straight  line,  thus  more  simply  producing  the  same  result 
as  the  sliding  wire  on  the  needle.* 

The  above  are  the  direct  tests  for  proportions,  and  if 
carefully  taken  should  give  the  correct  mass  of  the  drawing, 
but  for  the  smaller  proportions,  and  for  the  directions  of 
lines,  there  are  other  tests  Avhich  are  more  important.  The 
lines  with  which  it  is  most  natural  to  compare  directions 
are  vertical  and  horizontal  lines.  A  horizontal  line,  whose 
ends  are  equally  distant,  appears  horizontal,  and  is  repre- 
sented by  a  horizontal  line,  while  a  vertical  line  appears 
vertical,  and  is  represented  by  a  line  in  the  drawing  which 
is  perpendicular  to  the  horizontal.  If  a  straight-edge  be 
held  horizontal  with  its  ends  equally  distant  from  the  eye, 
it  will  represent  a  horizontal  line  in  the  drawing,  and  by 
looking  over  the  ruler  thus  held,  the  directions  of  lines  of 
the  object  may  be  compared  with  the  horizontal.  A  piece 
of  fine  thread  with  a  Aveight  attached  will  serve  as  a  plumb- 
line,  and  by  holding  it  in  front  of  the  object  its  lines  may 
be  compared  with  the  vertical.  The  thread  is  often  better 
than  the  rule  for  the  horizontal  line.  Care  must  be  taken 
to  hold  the  thread  perpendicular  to  the  line  of  sight.  This 
position  is  easiest  obtained  by  directly  facing  the  group 
and  extending  the  arms  equally,  so  that  both  ends  of  the 


*When  sketching  from  nature,  if  horizontal  edges  extend  on  both  sides  of  the 
spectator  and  it  is  desired  to  make  a  perspective  instead  of  a  model  drawing,  its 
dimensions  may  be  compared  by  holding  the  pencil  parallel  to  the  plane  on 
■which  the  drawing  is  supposed  to  be  made. 


TESTS.  59 

thread  are  the  same  distance  from  the  eye.  But  more  care 
must  be  exercised  to  get  the  thread  horizontal.  This  can 
only  be  done  by  looking  at  the  thread  alone,  until  it  is 
levelled,  when  the  student  may  look  behind.  If  this  is  not 
done,  the  lines  behind  will  be  most  likely  to  make  the  thread 
seem  horizontal  Avhen  it  is  not.  If  there  are  horizontal 
edges  behind,  which  are  parallel  to  the  picture,  they  will 
appear  horizontal,  and  will  place  the  thread  correctly,  but 
if  the  lines  are  not  directly  in  front  they  will  not  appear 
horizontal,  and  so  will  cause  the  thread  to  be  out  of  level. 

It  may  seem  that  unnecessary  space  has  been  given  to 
these  directions,  but  it  has  been  found  almost  impossible 
to  make  many  students  understand  the  matter,  and  hold  the 
thread  correctly,  even  with  repeated  explanations  and  illus- 
trations. Some,  after  months  of  study,  are  found  holding 
the  pencil  or  thread  at  an  angle  of  from  ten  to  twenty 
degrees  away  from  the  correct  position.  Hence  it  is  not 
thought  that  any  explanation  can  be  too  careful.  But  the 
problem  is  so  simple  that  any  student  who  wishes  to  suc- 
ceed should  have  no  difficulty  after  giving  careful  attention 
to  directions.  Of  this  the  student  may  be  sure,  that  he  will 
never  learn  to  draw  until  he  is  able  to  discover  his  mistakes, 
and  as  the  thread  is  a  most  important  test  it  should  be  cor- 
rectly applied. 

Any  object,  as  the  cube  (Fig.  96),  having  been  drawn,  it 
may  be  tested  by  the  thread  as  follows :  Hold  the  thread 
horizontal  to  cover  5,  and  note  its  intersection  with  1-6  and 
6-7.  Now  hold  the  plumb-line  so  as  to  cover  point  3,  and 
notice  where  it  intersects  5-6.     Then  hold  it  to  cover  6-7, 


60  TESTS. 

and  find  its  intersection  with  2-3.  Then  hold  the  thread 
to  cover  1  and  5,  also  2  and  4,  and  .compare  the  direction 
of  the  thread  with  the  horizontal.  Next  cover  2-7,  and  see 
where  this  line  continued  cuts  5-6,  then  4-7  to  intersect  2-1. 
Now  cover  in  succession  any  two  opposite  points,  as  1-3, 
and  3-6,  and  4-1,  etc.,  and  place  the  intersections  on  the 
inner  edges. 

Such  use  of  the  thread  is  simply  a  more  exact  method  of 
discovering  angles  than  drawing  the  lines  in  the  air  with 
the  pencil  point,  the  first  method  explained.  When  the  eye 
is  trained,  the  first,  which  is  of  course  the  simplest,  will  be 
all  that  is  needed.  But  most  students  will  find  the  use  of 
the  thread  preferable,  as  it  gives  a  fine  line  which  can  be 
made  to  exactly  cover  the  edges  of  the  object.  Its  inter- 
section also  with  the  edges  can  be  seen  much  more  readily 
than  that  of  a  line  formed  by  the  side  of  the  pencil,  whose 
size  hides  considerable  of  the  object.  If  these  tests  with 
the  thread  are  applied,  they  cannot  fail  to  discover  every 
error  of  importance. 

Another  and  last  test  may  be  made  by  holding  two  pen- 
cils, or  better  two  rulers,  together,  at  right  angles  to  the 
line  of  sight,  and  separating  them  until  one  covers  2-3,  and 
the  other  covers  5-6.  If  great  care  is  taken  the  directions 
of  these  lines  with  reference  to  each  other  may  be  seen,  and 
the  drawing  tested  by  continuing  these  lines  in  the  drawing. 

We  have  dwelt  thus  carefully  upon  each  test  to  be  applied 
in  the  hope  that  the  student  may  realize  their  importance, 
for  he  will  learn  to  draw  correctly  only  through  his  own 
efforts,  gaining  with  each  discovery  of  error.     He  can  never 


TESTS.  61 

become  a  draughtsman  as  long  as  he  depends  upon  a  teacher 
for  corrections.  Let  him  carry  his  drawing  so  far  that  a 
thorough  application  of  all  the  tests  explained  will  show 
no  error,  then,  as  it  is  simply  a  question  of  exactness  to  be 
determined  by  the  eye,  if  the  trained  eye  of  the  teacher 
discovers  mistakes  so  slight  that  the  student  cannot  rightly 
be  expected  to  determine  them  for  himself,  these  may  be 
pointed  out.  As  the  chief  benefit  results  from  what  the 
student  sees  and  does  himself,  he  will  be  much  better  off 
without  a  teacher  than  with  one  who  does  his  work  for  him. 
There  are  many  who  say  that  measurements  and  tests 
are  mechanical,  and  that  to  learn  to  draw  the  student  should 
draw  by  eye  simply.  It  is  true  that  measurements  and 
tests,  as  unfortunately  too  many  students  are  taught  to  use 
them,  cannot  fail  to  produce  hard  and  mechanical  drawings, 
and  retard  progress.  Still,  it  seems  better  for  the  student 
when  he  can  see  no  further  to  be  shown  by  tests  where  his 
eyesight  has  failed,  rather  than  to  carry  drawings  only  as 
far  as  he  can  by  eye  alone,  and  then  put  them  away,  and 
begin  others  which  can  be  carried  but  little  if  any  farther. 
Therefore  the  student  is  advised  to  apply  the  tests  ex- 
plained, after  he  has  carried  his  drawings  as  far  as  he  can 
see,  and  not  to  put  any  drawings  away  which  the  tests  show 
to  be  inexact.  This  training,  it  is  believed,  will  most 
quickly  produce  ability  to  draw  correctly  at  sight. 


THE  PLANE  OF  THE  DRAWING. 

The  mind  through  the  sense  of  sight  perceives  form,  the 
rays  of  light  from  any  object  entering  the  eye,  and  being 
focussed  on  the  retina,  and  forming  an  image  of  the  object 
as  in  the  camera,  except  that  in  the  latter  the  image  is 
formed  on  a  plane  surface,  while  that  in  the  eye  is  formed 
on  a  spherical  surface.  As  but  a  single  point  can  be  seen 
clearly  at  any  time,  the  image  of  the  eye  is  practically  the 
same  as  that  of  the  camera.  The  problem  for  the  artist  is 
to  make  his  drawing  so  that  it  shall  convey  the  same  idea 
of  form,  size  and  position  as  the  objects  which  it  represents. 
It  is  evident  that  this  must  occur  when  the  drawing  pro- 
duces the  same  image  in  the  eye  as  the  objects,  and  to  do 
this  the  drawing  must  be  similar  to  the  image. 

The  rays  from  any  object  to  the  eye  form  a  conical  body. 
If  this  cone  of  rays  be  intersected  by  any  plane  the  inter- 
section must  be  a  picture  of  the  object,  which  if  the  object 
be  taken  away  will  still  create  its  image  in  the  eye.  If 
this  plane  of  the  picture  be  at  right  angles  to  the  cone,  the 
section  (the  picture)  will  be  a  true  picture  of  the  object, 
that  is,  be  similar  to  the  image  of  the  eye.  In  Fig.  97  a 
circle.  A,  is  placed  vertical  and  in  front  of  the  eye.  In  the 
drawing  it  is  represented  by  line  A.  The  cone  formed  by 
the  rays  of  sight  is  represented  by  lines  b-b,  and  a  vertical 
plane  cutting  through  the  cone  of  rays  by  line  P.  If  the 
student  will  take  any  cone  and  hold  it  horizontal,  it  will 
perfectly  illustrate  the  figure,  the  base  of  the  cone  being 

(02) 


THE    PLANE   OF    THE    DRAWING.  63 

the  circle  A,  and  the  eye  being  at  the  apex.  "With  the  cone 
the  student  will  at  once  see  that  a  vertical  plane  between 
the  eye  and  the  base  of  the  cone  will  intersect  it  in  a  circle, 
and  this  circle  is  the  picture  of  the  base,  A. 

If  now  the  plane  of  the  picture  be  inclined  to  the  axis  of 
the  cone  (Fig.  98),  the  intersection  with  the  cone  will  still 
be  a  picture  of  the  circle,  but  in  shape  it  differs  from  that 
in  Fig.  97,  which  is  a  circle.  This  oblique  intersection  is 
seen  to  be  an  ellipse,  but  it  is  important  to  notice  that  it 
does  not  appear  so  to  the  eye  at  the  apex  of  the  cone,  but 
appears  a  circle  exactly  covering  the  base  of  the  cone.  It 
will  be  seen  that  it  makes  no  difference  how  the  plane  of 
the  picture,  P,  is  placed,  or  Avhat  the  proportions  of  the 
ellipse  resulting.  The  ellipse  always  must  appear  to  the 
eye  a  circle,  in  fact  the  circle  of  the  base,  A.  But  when  the 
eye  is  removed  from  the  apex  of  the  cone  the  ellipse  will 
appear  an  ellipse,  and  will  not  then  be  a  picture  of  the 
circle.  The  circle  of  Fig.  97  and  the  ellipse  of  Fig.  98  are  pic- 
tures of  the  circle  A,  and  both  create  in  the  eye,  when  at  the 
apex,  a  circular  image  of  the  circle,  but  the  former  only  is 
similar  to  the  object  A. 

In  looking  at  pictures  we  naturally  hold  them  in  front  of 
us,  and  at  right  angles  to  our  line  of  vision,  as  in  the  position 
of  the  plane,  P,  of  Fig.  97.  If  plane  P,  of  Fig.  98,  is  thus 
held,  the  ellipse  upon  it  will  be  seen  as  an  ellipse,  that  is,  will 
create  an  ellipse  as  image  in  the  eye.  This  cannot  create 
the  idea  of  a  circle.  We  see  that  the  first  picture  is  much 
preferable  to  the  second,  for  it  is  a  circle,  and  wherever  the 
eye  is  placed  will  create  a  circle  in  the  eye.    (It  is  of  course 


64  THE   PLANE    OF    THE    DRAWING. 

understood  that  it  is  always  looked  at  perpendicularly.)  The 
first  picture  Ave  will  distinguish  from  the  second,  and  from 
all  others  which  might  be  made,  by  calling  it  a  true  picture, 
meaning,  that  it  is  similar  to  the  image  created  in  the  eye 
by  the  object.  It  is  seen  that  there  can  be  but  one  position 
of  the  plane  which  will  give  a  true  picture,  and  this  must 
be  at  right  angles  to  the  direction  in  which  the  object  is 
seen.  The  plane,  of  course,  cannot  be  perpendicular  to  all 
the  rays,  and  by  this  is  meant  the  central  ray.  A  true 
picture  of  any  object  may  be  obtained  by  drawing  upon  a 
sheet  of  glass  with  a  brush  and  color,  or  a  pencil  of  soap, 
or  on  a  wire  screen  with  chalk,  the  glass  or  screen  being 
placed  at  right  angles  to  a  line  from  the  centre  of  the  object 
to  the  eye,  and  the  eye  and  screen  being  fixed  and  lines 
drawn  to  cover  all  the  edges  which  are  seen.  It  is  desired 
that  every  student  make  drawings  in  this  Avay,  a  small  pane 
of  glass  and  a  pencil  of  soap  being  the  best  materials.  The 
drawings  should  be  made  with  the  glass  at  right  angles  to 
the  rays,  and  also  when  held  obliquely,  so  that  the  drawings 
may  be  compared,  and  the  student  realize  that  the  glass 
must  be  perpendicular  to  the  direction  in  which  he  looks, 
for  the  drawing  to  give  the  real  appearance  of  the  object. 

It  will  appear  that  a  drawing  on  any  plane  or  surface  can 
create  the  correct  impression  only  Avhen  the  eye  is  in  the 
position  which  it  had  when  the  drawing  was  made.  All 
drawings,  then,  are  best  seen  from  some  one  point  or  distance. 
This  distance  the  trained  eye  will  naturally  select.  How- 
ever, as  draAvings  and  pictures  will  be  viewed  by  untrained 
eyes,  and  as  the  proper  point  may  not  always  be  accessible, 


THE    PLANE    OF    THE    DRAWING.  65 

it  is  very  important  that  all  be  avoided  which  will  cause 
marked  distortion  when  the  picture  is  not  seen  from  the 
proper  point.  If  the  picture  is  a  true  picture,  the  distortion 
produced  when  it  is  viewed  from  a  longer  or  shorter  dis- 
tance than  the  proper  one  will  appear  not  in  the  shape  of 
its  parts,  but  only  in  the  relative  sizes  of  the  objects  repre- 
sented. Thus,  the  distortion  of  a  true  picture  is  always 
less  than  that  of  a  drawing. on  a  plane  which  is  oblique  to 
the  rays,  and  so  the  true  picture  is  by  far  the  best  drawing 
that  can  be  made  for  general  use. 


REPRESENTATION. 


A  Paper  comparing  Perspective  and  Model  Drawing, 

READ  AT  THE  AnNUAL    MeETING  OF  THE  INDUSTRIAL 

Art  Teachers'  Association,  January  5,  1889. 


REPRESENTATION. 


This  term  includes  all  drawings,  constructive  and  decorative  works, 
being  as  fully  representations  as  perspective  views,  the  geometric  views 
conveying  ideas  of  facts  and  actual  dimensions,  the  pictorial  of  facts 
and  apparent  dimensions.  We  will  consider  simply  the  representation 
of  appearances,  and  our  subject  is  really  "  Pictorial  Drawing." 

The  aim  of  such  drawing  undoubtedly  should  be  to  awaken  in  the 
mind  of  the  beholder  the  same  impression  as  to  form,  size  and  position 
as  the  objects  themselves  would  create  when  viewed  from  the  artist's 
position.  Drawings  to  be  appreciated  require  certain  education  or 
qualities,  but  pictures  and  illustrative  drawings  are  so  numerous  that 
this  education  is  unconsciously  acquired,  and,  by  the  average  intellect, 
photographs  and  pictures  are  readily  understood. 

Photographs  and  drawings  such  as  isometric  are  often  very  different 
from  the  image  which  would  be  produced  upon  the  eye  by  the  objects, 
and  yet  they  are  accepted  without  difficulty,  the  mind  having  a  con- 
ception of  the  form  and  giving  to  the  drawing  the  most  reasonable 
interpretation;  so  that  a  quite  conventional  or  incorrect  drawing,  so 
far  as  appearances  are  concerned,  may  be  almost  as  readily  read  and 
accepted  as  one  more  nearly  agreeing  with  the  appearance.  This  does 
not  affect  our  decision  as  to  the  aim  of  the  artist ;  it  does,  however, 
assist  him  in  his  work,  which  otherwise  would  sometimes  be  nearly,  if 
not  quite,  impossible. 

A  drawing  which  produces  upon  the  eye  the  same  image  as  the 
object  must  be  one  whose  proportions  agree  with  the  appearance,  the 
angles  between  the  visual  rays  to  the  drawing  being  relatively  the 
same  as  between  the  rays  to  the  object.  If  the  horizontal  or  vertical 
angles  should  be  greater  to  the  drawing  than  to  the  object,  the  drawing 

(69) 


70  KEPRESENTATION. 

■would  be  correspondingly  too  wide  or  too  high.  In  the  light  of  this 
statement  let  us  consider  a  plane  perspective  drawing,  a  drawing  upon 
a  vertical  plane  in  which  the  eye  being  fixed,  each  line  of  the  drawing 
covers  the  edge  of  the  object  which  it  represents.  Fig.  1  is  a  pers. 
drawing  representing  vertical  and  horizontal  prisms.  Fig.  2,  which  is  a 
side  elevation,  shows  that  the  visual  rays  to  the  vertical  prism  intersect 
the  P.  PI.  obliquely,  and  that  the  measure  of  the  angle  between  them 
will  be  not  in  the  P.  PI.,  but  in  the  plane  L  M,  perpendicular  to  the 
rays,*  and  thus  the  perspective  drawing  A  is  too  high,  the  correct  height 
being  the  distance  1-2  and  the  difference  seen  by  comparing  A  with  B. 
Suppose  the  perspective  drawing  A  upon  the  vertical  plane  and  the 
shorter  B  upon  plane  L  M,  the  spectator's  eye  being  fixed  at  S.  P.,  both 
must  appear  alike,  and  convey  the  same  impression  as  the  object,  but 
as  ordinarily  viewed  from  a  point  not  S.  P.,  the  first  must  create  a 
wrong  impression  of  the  proportions  of  the  prism.  In  the  same  man- 
ner Fig.  3  proves  that  the  perspective  drawing  D  of  the  horizontal 
prism  is  too  wide,  E  being  the  real  appearance.  From  these  drawings 
we  see  that  a  plane  perspective  drawing  is  as  the  object  really  appears 
only  when  the  object  is  directly  in  front,  the  representation  of  objects 
in  all  other  positions  being  distorted,  vertically,  when  the  object  is 
above  or  below  C.  V.,  horizontally,  when  at  the  side,  and  obliquely, 
that  is  both  ways,  for  all  other  positions.  Of  course  when  the  eye  is 
at  S.  P.  the  distortion  is  not  noticed,  but  as  this  is  rarely,  perhaps 
never  the  case,  it  follows  that  a  perspective  drawing  generally  cannot 
give  a  correct  impression  of  the  sizes  of  the  objects. 

By  Fig.  2  we  find  that  a  drawing  of  the  prism  to  agree  with  the  ap- 
pearance must  be  made  upon  plane  L  M  at  right  angles  to  the  rays ; 
this  is  a  perspective  drawing  upon  a  plane  oblique  to  the  ground,  and 
as  parallel  retreating  lines  appear  to  converge  we  find  that  the  vertical 
edges  of  the  prism  which  are  oblique  to  the  P.  PI.  are  represented  by 
converging  lines.  Vertical  lines  must  appear  to  vanish  as  any  other 
retreating  lines,  but  in  order  that  these  lines  in  the  drawing  may  not 
seem  to  represent  edges  actually  inclining,  the  eye,  as  it  should  be  for 

*  The  central  visual  ray. 


REPRESENTATION.  71 

any  perpective,  must  be  at  S.  P. ;  from  any  other  position  the  drawing 
will  tend  to  give  the  impression  of  inclined  lines  in  nature,  which  is  as 
serious  a  matter  as  the  distortion  vertically  of  the  perspective  drawing 
upon  the  vertical  plane,  and  the  drawing  is  thus  no  better  than  the  first. 
Our  aim  is  to  obtain  a  drawing  which  may  be  viewed  naturally,  whose 
proportions  shall  agree  with  the  appearance  and  which  shall  give  a 
correct  impression  of  the  facts.  This  we  shall  accomplish  if  we  change 
the  drawing  B  by  substituting  vertical  for  the  inclined  lines  represent- 
ing the  vertical  edges.  Thus  corrected  we  will  call  it  a  "  model  draw- 
ing," which  term  we  use  in  the  sense  of  the  best  drawing — the 
drawing  which  to  the  ordinary  observer  shall  convey  the  same  idea  of 
form,  size  and  position  as  the  objects  themselves,  not  necessarily  a 
drawing  of  the  geometric  forms,  but  of  any  subject  whatever.  If  we 
attempt  to  make  such  a  drawing  from  an  extended  range  of  objects  we 
shall  find  that  the  P.  PI.,  in  order  to  be  at  right  angles  to  the  rays  to 
all,  will  become  the  surface  of  a  sphere ;  this  is  undevelopable  and 
although  a  drawing  might  be  made  which  would  give  the  exact  appear- 
ance of  every  object,  it  is  evident  that  it  could  not  give  the  relative 
positions,  and  would  be  no  more  a  picture  than  a  canvas  covered  at 
random  with  smaller  sketches.  It  follows  then,  that  a  drawing  which 
shall  comprise  a  wide  field  of  view  and  give  the  appearance  and  the 
relations  of  everything  drawn  is  an  impossibility. 

What  can  be  done  to  produce  a  drawing  whose  proportions  shall 
agree  with  the  appearance  and  which  shall  give  correct  information  of 
the  relations  of  objects  within  a  reasonable  limit  ?  There  is  often  less 
of  height  than  of  width  to  be  represented,  and  the  system  known  as 
curvilinear  perspective  results.  In  this  the  P.  PI.  is  vertical  and  cylin- 
drical, S,  P.  being  in  the  axis.  This  surface  is  developable,  and  a 
drawing  upon  it  will  have  its  horizontal  distances  correct,  though  the 
vertical  must  be  distorted  as  in  Fig.  1.  Fig.  4  is  a  plan  view  showing  S. 
P.,  the  curved  picture  plane  and  three  cubes.  The  P.  PI.  being  curved, 
the  angles  of  the  cubes  with  it  increase  with  the  distances,  and  in  the 
drawing  F  their  lines  converge  the  quicker  the  further  we  get  from  the 
cube  in  front,  and  thus  we  find  straight  lines  represented  by  curved. 


72  REPRESENTATION. 

This  drawing  will  give  the  impression  of  curved  lines  in  nature  and  is 
not  a  satisfactory  solution  of  the  problem,  the  perspective  drawing  G 
upon  plane  0  P  being  much  more  acceptable  in  its  representation  of 
parallel  straight  lines  by  straight  lines  converging  to  one  vanishing 
point.  Now  if  we  change  the  drawing  with  curved  lines  by  substituting 
straight  lines  tending  to  one  V.  P.,  we  shall  have  a  drawing  H  whose 
horizontal  distances  are  correct  and  which  gives  a  true  idea  of  the 
facts,  and  if  as  shown  by  Fig.  2  we  make  the  correction  for  the  heights, 
the  drawing  II  will  agree  in  proportion  with  the  appearance  and  will 
convey  correct  information  of  the  facts,  and  this  "  model  drawing " 
answers  the  conditions.  We  see  that  it  is  neither  a  plane  nor  a 
cylindrical  perspective,  but  a  combination  of  the  good  qualities  of  each, 
further  improved  by  having  the  vertical  dimensions  agree  with  the 
appearance.  It  may  be  considered  a  plane  perspective  whose  widths  and 
heights  have  been  corrected  to  agree  with  appearances.  This  drawing 
comes  very  near  to  perfect  agreement  with  appearances,  the  image 
created  by  it  upon  the  eye  being  practically  the  same  as  that  caused  by 
Nature  herself,  and  we  must  accept  it  as  the  best  possible  to  obtain. 

What  is  the  practice  of  our  illustrating  artists  ?  We  find  that  they 
do  not  measure  the  lengths  and  angles  of  all  lines,  and  constructing  a 
diagram  work  out  their  drawings  by  perspective  rule,  but  that  they 
generally  work  almost  entirely  by  appearances,  and  often  refuse  to 
admit  that  perspective  can  be  of  assistance  to  a  person  who  can  see 
and  who  wishes  to  record  his  feelings.  As  the  artist  endeavors  to 
represent  real  appearances,  the  sketches  illustrating  perspective  dis- 
tortions must  explain  why  his  opinion  is  thus.  Upon  examination, 
the  drawings  from  some  of  our  best  illustrators  will  be  found  to  be  so 
exact  as  regards  relative  proportion  and  direction  of  lines,  that  the 
curvature  resulting  from  representing  each  part  of  a  straight  line  as  it 
appears,  will  be  plainly  seen,  and  the  drawings  thus  are  good  examples 
of  curvilinear  perspective,  except  that  they  are  as  correct  vertically  as 
horizontally,  and  if  straight  lines  should  be  substituted  for  the  curved 
they  would  be  exactly  what  we  have  decided  to  be  the  best  representa- 
tion of  both  the  facts  and  the  appearances. 


REPRESENTATION.  73 

What  is  the  best  ti'aiaing  to  enable  one  to  draw  freely  and  correctly  ? 
The  artist  will  often  say,  "  continued  practice,"  and  consider  scientific 
study  of  little  or  no  value.  The  teacher,  will  say,  "  present  the  facts 
of  form  with  the  principles  of  perspective,"  and  each  will  argue  strongly 
that  his  method  is  the  most  satisfactory.  "We  must  judge  by  results, 
and  if  we  find  that  the  best  drawings  are  made  by  the  artists,  then 
their  opinions  are  entitled  to  consideration.  It  may  be  said  that  the 
artist  understands  how  to  draw  and  the  teacher  to  instruct,  and  that  we 
should  not  expect  to  compare  the  teacher's  drawing  with  the  artist's. 
Still  until  the  teacher  can  present  work  equalling  or  excelling  that  of 
the  artist  and  not  the  result  of  the  artist's  method  of  work,  an  im- 
partial judge  must  decide  that  any  criticisms  of  the  artist  have  founda 
tion. 

Representation  is  defined  as  the  art  of  delineating  objects  as  they 
appear  to  the  eye.  The  eye  sees  all  objects  as  surfaces,  the  mind  can 
only  infer  that  they  have  thickness,  and  thus  to  represent  the  appear- 
ance it  is  onl}'  necessary  to  determine  the  direction  which  the  edges 
appear  to  have.  For  this  the  artist  says,  "  practice,"  the  teacher, 
"  facts  of  form  and  perspective  principles,"  both  agree,  then,  that  the 
eye  unpractised  and  unassisted  is  not  to  be  depended  upon.  Two 
elements,  physical  and  intellectual  enter  into  all  drawing,  the  first,  the 
exercise  of  the  eye  and  hand,  the  second,  the  habit  of  observing  with 
exactness  and  memorizing  observations,  so  that  the  mind  may  com- 
pare and  reason,  the  latter  obviously  of  the  greater  importance :  the 
child  of  six  years  who,  seeing  a  drawing  carried  on,  said,  "  that 
drawing  was  thinking  and  then  drawing  aromid  the  think,"  having 
most  clearly  defined  the  subject. 

The  work  in  our  schools  is  based  upon  a  study  of  the  facts  of  form 
and  of  perspective  principles.  A  knowledge  of  the  facts  is  the  first 
obtained  by  the  student,  who  certainly  has  a  very  practical  idea  before 
a  study  of  theory  or  of  api^earance  may  be  made.  There  can  be  no 
question  but  that  this  knowledge  is  a  hindrance  when  he  attempts  to 
represent  the  appearance ;  thus  how  many,  if  any,  ever  represent  a 
foreshortened  horizontal  surface  by  too  little,  or  even  little  enough  of 


74  KEPRESENTATION. 

vertical  distance ;  and  who  ever  realized  without  a  special  effort  that 
the  long  axis  of  the  ellipse  representing  a  vertical  circle  above  or 
below  the  eye  is  not  a  vertical  but  an  inclined  line  (see  Fig.  5),  and 
the  tendency  must  always  be  that  the  image  of  the  eye  be  overthrown 
by  the  conception  of  the  mind.  Does  the  study  of  perspective  counter- 
act the  effect  of  this  knowledge  of  the  facts,  and  are  its  principles 
presented  in  a  way  to  assist  correctness  of  observation?  We  have 
seen  that  a  perspective  drawing  gives  the  real  appearance  only  when 
the  object  is  directly  in  front ;  the  illustrations  have  been  in  angular 
perspective,  but  the  study  is  introduced  by  parallel  perspective.  Fig. 
G,  K  is  a  parallel  perspective  drawing  of  a  cube.  In  this  the  edges 
parallel  to  the  P.  PI.  are  represented  by  horizontal  lines,  but  the  cube 
being  at  the  left,  three  faces  are  visible,  and  it  is  evident  that  these  lines 
can  not  appear  horizontal ;  the  real  appearance  is  shown  by  P,  and 
the  distortion  of  the  parallel  perspective  drawing  is  more  serious  than 
that  of  the  angular  perspective  drawing. 

Instrumental  perspective  introduced  by  numerous  drawings  in 
parallel  perspective  must  create  a  wrong  idea  of  the  appearance  of 
form.  This  is  generally  uncorrected  by  any  statement  of  the  instructor, 
and  the  knowledge  of  pers2)ective  attained  at  the  cost  of  an  entire  7nis- 
conception  of  appearances  can  he  of  little  value  in  free-hand  drawing. 
Instrumental  perspective  is  the  latter  part  of  our  public  school 
course.  Is  the  preceding  work  such  that  the  student  may  acquire  the 
power  of  careful  observation  which  is  not  given  by  the  study  of  the 
facts  of  form  or  of  perspective  1  We  find  that  as  in  perspective  later, 
the  first  work  is  from  objects  in  which  but  one  set  of  horizontal  lines 
vanish,  the  directions  being  to  draw  a  horizontal  line  representing  the 
level  of  the  eye  (the  horizon),  determine  the  proportions  by  pencil 
measurement,  and  see  that  the  retreating  edges  meet  at  a  point  in  the 
horizon.  So  many  illustrations  of  this  nature  are  to  be  found,  that  one 
wonders  where  the  favored  schools  may  be  which  have  plinths,  prisms, 
etc.,  for  every  student,  for  this  is  almost  a  necessity  where  neither  end 
of  the  object  is  to  be  seen,  and  if  not  thus  placed  the  drawings  made 
must  be  copies  of  the  illustrations  and  not  from  the  object.    Next 


REPRESENTATION.  75 

comes  the  use  of  two  vanishing  points,  as  before  the  horizon  is  first  to 
be  drawn,  and  the  retreating  edges  are  to  meet  at  points  in  this  line, 
their  angles  being  determined  by  strips  of  paper  held,  one  horizontal 
and  the  other  to  cover  the  edges.  It  is  easy  for  the  student  to  follow 
these  directions  so  that  perspectively  the  drawing  is  correct ;  but  is  it 
easy  to  determine  how  far  below  the  horizon  the  drawing  shall  be 
placed,  or  where  between  the  vanishing  points  1  Directions  (measure- 
ments) may  be  given,  but  if  so  he  is  not  making  the  drawing ;  and  if 
he  measures  the  angles  of  the  retreating  edges  and  continuing  them  to 
cut  the  horizon  thus  locates  the  points,  how  may  he  be  sure  of  the 
angles  ?  Certainly  not  by  the  use  of  the  paper  strips.  This  must  be 
admitted  by  any  candid  observer  who  has  seen  students  measuring 
proportions  and  angles  with  the  pencil  or  paper  held  parallel  to  retreat- 
ing edges,  and  in  all  positions  except  correctly  at  right  angles  to  the 
line  of  sight.  From  the  beginning  of  this  free-hand  work,  perspective 
principles  are  explained  and  all  the  illustrations  and  explanations  give 
the  student  the  impression  that  the  drawing  is  made  upon  a  vertical 
plane,  and  this  the  student  comes  to  think  of  as  parallel  to  the  wall  of 
the  room  or  to  the  edge  of  the  table  supporting  the  group ;  an  inevit- 
able conclusion  by  which  the  plane  for  almost  all  is  from  20°  to  45° 
away  from  the  position  which  will  give  the  correct  appearance ;  and  it 
seems  that  perspective  is  made  an  instrument  whereby  a  certain  number 
of  drawings  may  be  produced,  which  the  students  accept  as  the  appear- 
ance of  the  objects  from  which  they  are  supposed  to  be  drawing,  the 
teachers  evidently  thinking  that  so  long  as  perspective  principles  are 
illustrated  the  discrepancy  between  the  perspective  drawings  and  the 
actual  appearance  is  of  no  consequence.  In  the  work  from  groups 
following  there  is  a  difference  of  opinion  as  to  the  steps.  Some  say 
draw  the  upper  object  first,  others,  the  lower  or  principal  one.  This  is 
an  interesting  question  in  view  of  the  statement  so  strongly  made  by 
educators  that  a  subject  must  be  considered  as  a  whole  before  its  parts 
are  taken  up,  and  yet  we  are  told  that  we  must  determine  the  width 
and  length  of  each  object  before  beginning  to  draw,  and  there  is  no 
certainty  as  to  whether  we  shall  draw  first,  the  upper,  lower,  or  yrinci- 


76  REPRESENTATION. 

pal  object.  If  the  statement  that  a  subject  must  first  be  treated  as  a 
whole  is  true  in  one  case,  it  must  be  for  all,  and  especially  for  art,  and 
•without  further  dicussion  the  absurdity  of  these  questions  is  made 
evident.  But  we  will  now  follow  a  student  in  his  study  of  the  group 
of  models  illustrated  by  Fig.  7.  Following  the  directions  given,  the 
student  draws  the  vase  first,  determining  its  width  and  height  and  get- 
ting the  outlines  symmetrical  about  the  vertical  centre  line ;  this  done 
he  takes  the  prism,  then  the  cylinder  and  last  the  frame,  treating  each 
in  the  same  manner  as  the  vase.  What  is  the  result  ?  —  He  completes 
his  drawing  before  he  can  tell  whether  its  entire  width  is  correct  for  its 
height,  and  often  without  even  considering  the  question,  and  working 
as  he  does,  is  led  to  think  of  the  appearance  of  each  object  by  itself, 
and  not  in  its  relation  to  the  whole.  The  proportions  of  each  object 
having  been  determined  before  drawing  there  is  nothing  to  be  done 
but  to  make  the  drawing  to  these  measurements.  He  does  not  under- 
stand that  measurements  at  best  can  only  assist  not  perform  the  work 
of  the  eye,  and  that  as  he  depends  upon  them  they  are  more  likely  to 
give  incorrect  than  correct  results ;  but  he  makes  the  drawing,  thinking 
that  since  each  object  is  made  of  its  determined  proportions  that  when 
the  last  is  complete,  the  group  must  be  correct,  and  though  perhaps  a 
suspicion  that  it  is  not,  flashes  upon  him  as  he  surveys  the  finished 
drawing,  he  refuses  upon  reflection  to  entertain  the  idea,  for  has  he 
not  made  sure  of  each  object  as  he  drew  it,  and  the  thought  of  erasing 
his  finely  finished  lines  convinces  him  that  if  his  di-awing  does  seem  a 
little  queer  it  is  correct,  and  that  he  cannot  see  rightly.  This  drawing, 
a  whole  obtained  by  considering  and  adding  to  one  another  its  various 
parts,  entirely  out  of  proportion,  awkward  and  mechanical,  is  put  away 
as  a  work  of  art,  and  we  find  that  the  free-hand  work  is  free-hand 
perspective  and  not  model  drawing,  that  the  power  of  observation  has 
not  been  trained  or  depended  upon,  that  perspective  rules  come  first 
and  cause  a  subordination  of  appearances  to  mechanical  and  uneduca- 
tional  means,  and  as  a  result  the  student  even  after  graduating  has  no 
facility  in  drawing,  and  if  put  before  a  new  subject  is  entirely  at  a  loss 
4s  to  how  to  proceed.     Is  it  to  be  wondered  at,  if  in  continuing  this 


REPRESENTATION.  77 

•work  and  being  brought  to  practically  consider  these  questions,  and  to 
discover  that  he  has  been  working  in  ignorance  he  decides  that  per- 
spective is  a  snare  to  be  carefully  avoided  ? 

Having  seen  that  perspective  dravrings  are  distortions  and  having 
followed  the  changes  in  tlie  positions  of  the  plane,  and  the  corrections 
by  which  a  model  drawing  is  produced,  is  it  possible  to  explain  them 
to  the  student  and  to  make  model,  instead  of  perspective  drawings  ?  I 
answer  to  the  first  part  of  this  question,  most  decidedly  no,  but  that 
this  is  not  necessary  or  at  first  desirable,  and  that  it  is  possible  to  teach 
mod'el  drawing  loithout  this  special  theoretical  consideration  of  the  plane 
of  the  drawing  or  of  perspective  principles,  and  that  practically  the 
differences  resulting  from  a  change  in  the  position  of  the  plane  can 
be  shown  as  follows:  Give  the  student  a  frame  covered  with  wire 
gauze,  and  have  him  mark  upon  it  the  appearance  of  the  object,  the 
frame  being  held  vertical  or  in  any  position  oblique  to  the  visual  rays, 
and  then  at  right  angles  to  the  same.  On  comparing  the  drawings,  the 
student  will  readily  see  that  only  the  latter  gives  the  real  appearance, 
and  as  a  result  of  this  experiment  will  understand  that  the  pencil, 
where  measurements  are  taken,  must  be  perpendicular  to  the  direction 
in  which  he  looks,  and  that  when  held  horizontal  in  this  position,  it 
will  be  represented  by  a  horizontal  line,  as  will  also  any  line  of  the  ob- 
ject which  it  then  appears  to  cover.  Having  realized  this  most  im- 
portant point,  which  the  present  teaching  never  does,  our  aim  should 
be  that  the  student  acquire  as  quickly  as  possible  the  ability  to  see 
correctly,  and  not  at  first  abstractions  and  theories,  but  facts  of  ap- 
pearances. This  power  of  correct  observation  must  be  the  result  of  a 
continued  perception,  through  his  own  efforts,  of  the  imperfections  of 
previous  observations.  It  follows,  then,  that  we  must  furnish  practical 
means  for  correction  and  be  sure  that  their  proper  use  is  understood. 
The  pencil  and  a  thread  with  weight  attached  are  all  that  is  required 
and  may  be  used  as  follows,  see  Fig.  9.  The  outline  of  the  appear- 
ance should  first  be  sketched  by  eye,  and  then  tested  by  the  pencil,  its 
entire  height  with  the  width,  then  all  visible  lines  lightly  sketched  and 
the  test  made  by  holding  the  pencil  or  thread  horizontal,  and  thus 


78  REPRESENTATION. 

taking  horizontal  lines  through  the  angles  of  the  object  and  noting 
where  these  lines  cut  the  front  and  opposite  side,  and  comparing  with 
the  drawing.  It  is  almost  impossible  for  many  students  to  hold  the 
pencil  correctly  at  right  angles  to  their  line  of  sight,  but  this  difficulty 
may  be  avoided  by  driving  a  large  needle  exactly  at  right  angles  into 
the  centre  of  the  pencil ;  when  only  its  end  is  seen  the  pencil  is  in  the 
proper  position.  By  the  plumb-line  vertical  lines  may  be  taken  through 
the  angles  of  the  objects,  and  the  points  where  they  cut  the  opposite 
side  noted  as  of  the  horizontal  lines.  These  tests  are  simple  and  will 
discover  all  mistakes,  but  to  insure  correctness  the  thread  may  be  held 
to  cover  and  continue  all  edges  of  the  object  so  that  their  intersections 
with  the  opposite  side  may  be  noted,  the  direction  of  diagonals  and 
of  any  lines  whatever  connecting  points  on  opposite  sides  be  deter- 
mined, and  their  intersections  with  intermediate  lines,  and  last  two 
straight  edges  held  to  cover  any  two  parallel  lines  will  show  the  appar- 
ent angles  between  them.  These  tests  will  surely  point  out  any  differ- 
ences between  the  drawing  and  the  appearance  and  are  all  that  should 
be  employed  until,  the  student  having  acquired  control  of  the  means 
and  being  able  to  make  fairly  good  drawings,  occasion  may  be  taken, 
as  the  nature  of  the  drawing  presents,  to  call  attention  to  perspective 
principles  which  are  illustrated  in  the  finished  sketches,  but  it  will  be 
better  to  delay  such  explanation  than  to  incur  the  risk  that  the  stu- 
dents may  utilize  the  principles  to  avoid  the  careful  observation 
necessary  to  give  correct  judgment  and  freedom  in  drawings.  Draw- 
ings made  in  this  way  may  not  at  first  be  as  successful  perspectively 
as  if  drawn  by  rule  and  the  vanishing  points,  but  they  will  be  much 
more  educational  and  will  enable  the  student  to  see  correctly,  that  is 
to  accept  the  image  of  his  eye  as  the  real  appearance.  It  will  be  seen 
that  the  use  of  the  thread  in  this  way  lays  especial  importance  upon 
the  actual  construction  (the  facts),  as  an  aid  to  its  representation 
(thus  continuing  all  edges  and  diagonals  and  noting  intersections,  is 
simply  making  use  of  the  actual  construction  to  test  its  representation), 
but  in  all  cases  the  drawing  should  be  made  by  the  eye  before  any  tests 
are  applied.    The  eye  should  be  depended  upon  and  thus  trained  to 


REPRESENTATION.  70 

correct  observation  before  abstract  principles  are  presented,  I  should 
rather  saj^  let  the  principles  present  themselves,  or  be  deduced  from 
the  drawings,  as  may  easily  be  done,  for  instance  —  when  a  drawing 
representing  several  parallel  horizontal  lines  whose  V.  P.  comes  on 
the  paper  has  been  completed,  the  student  may  be  shown  that  these 
lines  continued  intersect,  and  that  the  point  is  on  a  level  with  his  eye. 
In  this  way  by  practically  discovering  perspective  truths  they  will  be 
understood  in  such  a  way  as  to  be  of  value. 

Fig.  9  shows  this  method  applied  to  the  group  before  considered. 
The  proportions  of  the  whole  group  being  first  sketched  by  light  lines 
joining  the  principal  points,  the  entire  width  and  height  then  deter- 
mined as  carefully  as  possible,  and  the  objects  then  drawn  all  at  once, 
by  seizing  the  important  lines  of  each  and  considering  them  with  refer- 
ence to  the  group  as  a  whole,  the  cord  being  frequently  used  as  ex- 
plained to  determine  the  correctness  of  recorded  observations.  The 
pencil,  which  must  be  long,  being  held  freely  and  the  lines  drawn  with 
a  quick  movement,  and  when  found  to  be  incorrect  others  drawn  be- 
side them,  until,  the  proper  position  having  been  verified  by  careful  use 
of  the  thread,  all  other  lines  are  erased  at  one  time.  Working  in  this 
way  the  student  not  having  the  false  idea  that  it  is  possible  to  deter- 
mine exact  proportions  and  slight  differences  before  drawing,  will  de- 
pend more  upon  sight,  will  expect  to  change  his  first  lines,  and  will  do 
so  as  each  test  indicates.  He  will  soon  find  that  each  line  tests  many 
others,  that  he  can  see  more  readily  than  measure  the  fine  effects  nec- 
essary to  exactness,  and  that  a  group  is  not  more  difficult  than  a  single 
object.  It  will  not  be  necessary  for  the  vanishing  points  to  come  on 
the  paper  that  he  may  be  sure  of  his  drawing,  or  that  he  crawl  over  a 
floor  twenty  feet  square  used  as  a  drawing  board  to  test  a  half  impe- 
rial paper.  In  this  connection  I  wish  to  suggest  that  if  instead  of  lin- 
ing in  with  lines  of  one  strength,  or  conventionally,  the  nearer  edges 
being  represented  by  the  stronger  lines,  the  students  are  made  to  study, 
and  represent  the  edges  as  they  appear,  some  brought  out  by  shade  or 
shadow  strongly,  others  in  the  light  or  shade,  and  perhaps  barely  visi- 
ble, lightly,  they  will  be  started  in  the  direction  in  which  only  they  can 


80  REPRESENTATION. 

advance  and  make  artistic  sketches  from  nature,  and  the  observation 
involved  will  be  of  the  greatest  value  when  light  and  shade  is  taken 
up.  This  dependence  upon  sight  trained  by  these  tests  is  the  only  way 
to  prepare  for  practical  work  from  nature,  and  the  student,  whatever 
his  training,  who  acquires  facility,  must  come  to  depend  upon  it  largely, 
and  any  one  who  attempts  to  formulate  rules  to  govern  the  production 
of  art  works  will  soon  find  his  task  beyond  him. 

It  may  be  said  that  this  dependence  upon  individual  observation  is 
not  possible  for  public  school  work  as  each  student  would  require  at- 
tention which  it  would  be  impossible  for  him  to  receive.  Although 
this  objection  has  force,  still  there  is  no  doubt  that  the  proper  use  of 
the  thread  and  pencil  could  be  insisted  upon  by  the  teachers  and  se- 
cured ;  this  attained,  the  efforts  of  the  students  would  be  in  the  right 
direction,  and  if  not  perfect,  would  be  more  valuable  than  any  attempt 
to  work  by  rules  which  in  most  cases  can  be  simply  memorized,  not 
understood. 

Having  seen  that  the  study  of  the  facts  of  form  and  perspective 
causes  a  neglect  of  appearances,  and  the  working  in  an  impractical  way, 
shall  we  decide  that  perspective  and  science  are  useless?  Because  per- 
spective drawings  to  give  the  correct  impression  require  to  be  seen  from 
S.  P.,  and  because  perspective  principles  have  been  misused,  are  not 
sufficient  reasons  for  not  teaching  the  subject.  As  shown  in  the  first 
illustrations,  drawings  must  conform  to  perspective  principles  to  be  ac- 
ceptable and  some  drawings  must  be  parallel  perspective.*     A  knowl- 

*See  Fig.  10  which  represents  the  two  nearer  cubes  shown  in  Fig.  4,  and  a  third 
cube  at  the  riglit  of  the  spectator  and  in  line  with  the  others.  We  have  seen  that 
representing  straight  lines  as  they  appear  (curved)  is  not  acceptable  and  we  must 
determine  the  direction  of  a  straight  line  which  shall  represent  the  horizontal 
edges  nearest  parallel  to  the  spectator.  It  is  evident  that  a  horizontal  line  will 
equalize  the  distortion  and  give  the  most  satisfactory  result,  and  whenever  ob- 
jects are  in  line  with  one  another  and  on  each  side  of  the  spectator  this  drawing 
must  generally  be  made.  1  Bay  generally  because  the  judgment  and  good  sense 
of  the  artist  should  be  depended  upon  and  in  drawings  from  large  subjects  out 
of  doors  where  the  lines  are  broken  the  curvature  of  the  lines  may  not  be  noticed 
and  may  sometimes  give  the  best  result,  as  much  in  Fig.  10  as  in  Fig.  4.     In  Fig. 


RETKESENTATIOX.  81 

edge  of  perspective  must  then  assist  the  draughtsman,  and  as  a  study 
to  be  taken  up  after  tlie  students  have  acquired  ability  to  represent 
appearances  fairly  well,  and  with  the  distinct  understanding  that  per- 
spective drawings  do  not  do  this,  I  think  that  perspective  should 
be  taught,  just  when,  depending  upon  circumstances,  although  it  seems 
that  in  all  but  the  higher  grades  the  time  might  be  given  with  better 
advantage  to  model  drawing. 

We  have  stated  that  many  illustrations  are  so  correct  in  representing 
the  exact  appearance  of  nature  that  the  apparent  curvature  of  straight 
lines  may  be  seen.  On  the  contrary  many  more  drawings,  while  in  the 
main  correct  as  to  proportions,  are  so  full  of  discrepancies  that  hardly 
three  of  a  system  of  parallel  lines  can  be  found  to  intersect  at  the  same 
point,  and  often  these  points  for  horizontal  lines  will  be  above  or  below 
the  horizon,  and  geomi'tric  forms  are  distorted.  Errors  such  as  these, 
of  greater  or  less  importance,  are  to  be  found  in  the  work  of  even  the 
best  illustrators  and  noted  artists,  the  most  perfect  eye  with  the  long- 
est training  not  being  surety  against  carelessness   or   the  influence 

10  the  question  will  arise  shall  we  make  a  perspective  drawing  throughout  or 
shall  the  foreshortening  of  horizontal  distance  at  tlic  right  and  left,  and  of  verti- 
cal distance  above  and  below  the  centre  be  given.  This  again  is  a  question  which 
the  artist  must  decide  as  each  case  arises.  But  for  the  woilv  in  the  public  schools 
it  is  not  necessary  that  the  question  bo  considered  —  lot  straight  lines  be  repre- 
sented by  straight  lines,  straight  lines  extending  on  each  side  by  horizontal  lines 
and  insist  upon  ihe  pencil  being  always  at  right  angles  to  the  visual  rays  when 
measurements  are  taken,  and  unless  an  unusually  bright  student  draws  from  a 
cube  directly  in  front  so  that  he  sees  only  the  top  and  front  (faces,  the  question 
will  never  occur  as  the  foreshortening  of  the  vertical  face  is  so  little  ordinarily 
that  in  any  figure  except  the  square  it  will  be  hardly  noticed. 

It  will  be  seen  that  parallel  perspective  introduces  many  more  puzzling  ques- 
tions than  angular,  and  if  objects  are  to  be  drawn  with  only  two  faces  visible  it 
would  be  well  not  to  take  the  cube,  as  the  student  should,  from  the  first  and  all 
the  time,  be  made  to  determine  the  angular  dimensions  of  the  apisearancc  of 
objects,  which  can  only  be  done  with  the  pencil  held  at  right  angles  to  the  rays 
to  the  parts  as  they  are  drawn,  and  when  he  completes  his  course  he  should  bo 
able  to  harmonize  these  dimensions  with  perspective  appearances  which  are  nec- 
essary to  most  drawings. 


82  REl'KKSKNTATIOX. 

which  one  line  has  to  change  the  apparent  direction  of  another.  We 
remember  the  criticism  of  a  picture  which  showed  tlie  full  moon  and 
setting  sun  in  one  sky.  This  is  no  more  serious  a  contradiction  than 
many  which  are  apparently  unnoticed,  such  as  shadows  or  sunlight  in 
the  shade,  and  the  shadows  in  part  of  a  picture  advancing,  indi- 
cating the  sun  in  front  of  the  spectator,  while  in  another  part  they  re- 
treat and  show  the  sun  behind.  These  mistakes  may  pass  unnoticed 
because  of  an  uneducated  or  lenient  public,  still  there  can  be  no  ques- 
tion but  that  the  drawings  would  be  better  true.  Perspective  is  the 
remedy  for  such  mistakes,  and  an  extensive  scientilic  knowledge  is  not 
required  ;  no  more  is  really  necessary  than  an  observance  of  the  princi- 
ples as  they  are  illustrated  in-  the  simplest  sketches  which  may  be  made 
from  nature,  though  there  can  be  no  question  but  that  the  broader  the 
knowledge  the  better,  and  that  a  course  in  plane  and  solid  geometry, 
especially  intersections,  perspective,  shadows,  reflections,  etc.,  will 
benefit  any  draughtsman.  He  may  not  apply  or  make  use  instrument- 
ally  of  his  knowledge,  but  unconsciously  as  he  works  its  influence, 
will  produce  drawings,  which,  while  giving  the  proportion  and  the  feel- 
ing will  not  transgress  laws  of  nature  or  of  perspective,  but  in  design- 
ing it  will  have  its  greatest  value,  since  when  nature  cannot  be  studied 
knowledge  must  be  depended  upon. 

We  must  conclude  then,  that  the  best  method  of  instruction  is  that 
which  adds  to  a  practical  way  of  working  from  the  object,  a  knowledge 
of  the  facts  of  form  and  of  perspective  principles,  which  may  supple- 
ment the  power  of  sight  to  produce  correct  drawings. 

In  closing  I  quote  a  sentence  from  a  work  of  the  18th  century  by 
Gerard  DeLaircsse  :  "  I  conclude  then,  that  pictures  exhibiting  nature 
contrary  to  what  she  ought  to  be  are  liable  to  censure,  and  that  we 
ought  to  seek  the  truth  by  reasoning,  and  then  waiving  old  customs 
and  prejudice  to  believe  our  own  eyes." 

ANSON  K.  CROSS. 

Boston,  December,  1888. 


NOTE. 


The  illustrations,  which  have  been  reduced  from  the  hasty  sketches  prepared 
for  blackboard  use,  are  from  the  notes  for  the  perspective  lectures  which  have 
been  given  the  last  four  years  in  class  B  of  the  Massachusetts  Normal  Art  School. 


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